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Topic: Cubic graph

Related Topics

Petersen graph

Glossary of graph theory

Graph homomorphism

Chromatic number

Chromatic index

Graph theory

Crossing number

Symmetric group

	Cubic graph - Wikipedia, the free encyclopedia
		In the mathematical field of graph theory, a cubic graph is a graph where all vertices have degree 3.
		A bicubic graph is a cubic bipartite graph.
		In 1971, Tutte conjectured that all bicubic graphs are Hamiltonian.
	en.wikipedia.org /wiki/Cubic_graph (163 words)

	Petersen graph - Wikipedia, the free encyclopedia
		The Petersen graph is a small graph that serves as a useful example and counterexample in graph theory.
		is the smallest cubic graph of girth 5.
		Among the generalized Petersen graphs are the n-prism G(n,1), the Dürer graph G(6,2), the Möbius-Kantor graph G(8,3), the dodecahedron G(10,2), and the Desargues graph G(10,3).
	en.wikipedia.org /wiki/Petersen_graph (730 words)

	Cubic graph: Facts and details from Encyclopedia Topic (Site not responding. Last check: 2007-10-20)
		In the mathematical field of graph theory the degree or valency of a vertex v is the number of edge (graph theory)edges incident to v (with loop...
		In graph theory, a regular graph is a graph where each vertex has the same number of neighbors....
		In the mathematical field of graph theory, a hamiltonian path is a path in a undirected graph which visits each vertex exactly once....
	www.absoluteastronomy.com /encyclopedia/c/cu/cubic_graph.htm (365 words)

	Combinatorics Seminar - Fall 2005
		We construct a connected cubic graph on 60 vertices with domination number 21 and a sequence of connected cubic graphs where the limit of the ratio of the domination number to the number of vertices is at least 8/23, which equals 1/3+1/69.
		An edge-labeling of a graph G is a bijection from E(G) and 1,...,E(G)
		The edge-bandwidth of a graph G is the minimum bandwidth among all edge-labelings.
	www.math.uiuc.edu /~jozef/seminar/fall2005.html (1686 words)

	Cubic Cages
		The graph is not vertex-transitive having orbits of length 8 and 16.
		Collapsing the triangles to a vertex yields a 2688-vertex graph with diameter 14 and girth 18.
		A smallest graph of girth 10 and valency 3.
	www.csse.uwa.edu.au /~gordon/cages (2642 words)

	Regular graph: Encyclopedia topic (Site not responding. Last check: 2007-10-20)
		Regular graph of degree at most 2 are easy to classify: A 0-regular graph consists of disconnected vertices, a 1-regular graph consists of disconnected edges, and a 2-regular graph consists of disconnected cycle (cycle: A single complete execution of a periodically repeated phenomenon) s.
		A 3-regular graph is know as a cubic graph (cubic graph: in the mathematical field of graph theory, a cubic graph is a graph where all vertex...
		The smallest graphs that are regular but not strongly regular are the cycle graph (cycle graph: in the mathematical field of graph theory a cycle graph or circle graph is a graph...
	www.absoluteastronomy.com /reference/regular_graph (263 words)

	Petersen (Site not responding. Last check: 2007-10-20)
		The Petersen graph is the complement of the Johnson graph J(5,2).
		The Petersen graph is also a cage (graph with smallest possible number of vertices given its valency and girth).
		The Petersen graph is contained in the complement of the Clebsch graph and the Sp(4,2) Generalized Quadrangle and the Hoffman-Singleton graph.
	www.win.tue.nl /~aeb/drg/graphs/Petersen.html (346 words)

	Cages (Site not responding. Last check: 2007-10-20)
		A (k,g)-cage is a regular graph of valency k and girth g and minimal number of vertices.
		Robertson, The smallest graph of girth 5 and valency 4, Bull.
		Wegner, A smallest graph of girth 5 and valency 5, J.
	www.win.tue.nl /~aeb/drg/graphs/cages.html (703 words)

	Gordon Royle's Cubic Graphs
		The cubic graphs on up to 20 vertices, together with some smaller families of high girth cubic graphs on higher numbers of vertices are available.
		The really important part of this definition is that the graph has chromatic index 4; the statement that all cubic graphs of chromatic index 4 are non-planar is equivalent to the four-colour theorem, and hence a planar snark (a boojum) would be a counterexample to the four-colour theorem.
		Gunnar Brinkmann's cubic graph generation program was used to construct snarks of all orders up to 28.
	www.csse.uwa.edu.au /~gordon/remote/cubics (737 words)

	Honours Projects available - 1997-98 (Site not responding. Last check: 2007-10-20)
		Cubic (or 3-regular, 3-valent) graphs are those in which every vertex is adjacent to exactly 3 other vertices.
		Since every n-vertex cubic graph has exactly 3n/2 edges it is not clear whether this problem exhibits a phase transition (since there seems to be no natural parameter to vary with respect to the number of vertices).
		Preliminary studies, however, involving a standard algorithm for randomly generating cubic graphs indicate possible route to resolving the question of parameter selection: namely the random generation algorithm indicates that cubic graphs can be represented by a finite code.
	www.csc.liv.ac.uk /~ped/projects/projlist.html (435 words)

	[No title]
		The combinatorial structure of a graph drawn on the sphere is represented by the cyclic order of the edges at each vertex, where (according to the arbitrary choice we will adopt) the order is clockwise if we look at the sphere from the outside.
		The dual of a triangulation is an imbedded cubic (trivalent) graph.
		In the case of triangulations, this calculation yields the number of faces, which is the number of vertices in the dual cubic graph.
	prolland.free.fr /works/research/MPG5/doc/plantri-guide.txt (3797 words)

	Function (mathematics) - Wikipedia, the free encyclopedia
		The graph of a function f is the set of all ordered pairs (x, f(x)), for all x in the domain X.
		If X and Y are subsets of R, the real numbers, then this definition coincides with the familiar sense of "graph" as a picture or plot of the function, with the ordered pairs being the Cartesian coordinates of points.
		Sometimes a function can be modified, often by replacing the domain with a subset of the domain, and making corresponding changes in the codomain and graph, so that the modified function has an inverse that is a function.
	en.wikipedia.org /wiki/Function_(mathematics) (3304 words)

	A) y = 1/(x + 7) A vertical asymptote at x = -7 (Site not responding. Last check: 2007-10-20)
		This is a cubic graph shifted left by 8 and up by 4.
		The graph is concave upward because the power is greater than 1.
		The difference in degree is 2 and thus the end behavior of the graph is to follow a parabola.
	users.stlcc.edu /amosher/MatchGraphISoln.htm (731 words)

	Prism Graphs
		A prism graph is obtained from a prism by adding a series of horizontal edges on lateral faces.
		Cubic 3-connected graphs of bandwidth 3 are characterised using a special class of prism graphs, known as Fibonacci prisms.
		When we build a cubic graph labeled for bandwidth 3 and 3-connected we may think of the general step to be represented as a cubic graph H with some dangling edges.
	vega.ijp.si /htmldoc/manual/PRISM.HTM (1522 words)

	Week 3 Abstracts
		The random bipartite model G(n,n,p) is a probability space, whose elements are labeled bipartite graphs with vertex classes A and B, both of size n, where a vertex from A and that from B are connected by an edge randomly and independently with probability p=p(n).
		We prove that every graph on the Klein Bottle which does not contain contractible cycles of length 3 or 4 is either 3-colorable or has a subgraph isomorphic to a member of a particular family of non-3-colorable graphs.
		The Kneser graph K(n,k) is the graph of the disjointness relation on the k-element subsets of an n-set.
	dimacs.rutgers.edu /drei/1998/week3.html (3950 words)

	fulker (Site not responding. Last check: 2007-10-20)
		A cubic graph is one that is regular of degree three.
		The Petersen graph is not a counterexample (so the conjecture must be true!); the six 1-factors form such a double cover.
		[Se] P.D. Seymour, On multi-colourings of cubic graphs, and conjectures of Fulkerson and Tutte, Proc.
	www.emba.uvm.edu /~archdeac/problems/fulker.htm (366 words)

	Math3343 Assignment 3, Fall 2002
		The girth of a graph is the length of its shortest cycle.
		Prove that if you two color the edges of a complete graph on 10 vertices with the colors red and blue, there will be either a triangle colored blue, or a subgraph isomorphic to the complete graph on 4 vertices with all its edges colored red.
		First note the the line graph of a connected graph is also connected, because following a trail in a graph is like following a path in the line graph.
	www.cs.unb.ca /profs/horton/math3343/solutions3.html (665 words)

	CATS Fall 2002 abstracts
		Given a graph G, an acyclic set A in G is a subset of V(G) such that the induced graph on A is acyclic.
		The graph algorithm for solving the problem of separating Y from B ions in a set of mass spectra will be presented.
		We represent mass spectral data as a graph, considering each spectral peak as a node and relationship between two spectral peaks as a type-1 edge if suspected to be of the same ion type or as a type-2 edge if suspected to be of different types of ions.
	www.cs.uga.edu /~rwr/Seminar/F03.html (1255 words)

	write up 1 (Site not responding. Last check: 2007-10-20)
		Variable B: We can conclude from the data and graph that the variable b in the equation y=ax+b is the point where the graph of the line crosses the y-axis, also known as, the y-intercept.
		Variable B: We can conclude from the data and graph that when b is a positive number it causes the original graph to curve up into the second quadrant, therefore causing two x-axis intersection points.
		The constants b and c in the cubic equation struggle to draw comparisons to the linear equation.
	www.auburn.edu /~scherjm/writeup1/writeup1main.htm (989 words)

	Problem (Site not responding. Last check: 2007-10-20)
		This conjecture is attributed to Berge in [2].
		Every 2-connected cubic graph has a collection of five perfect matchings that together cover all edges of the graph.
		[2] P.D. Seymour, On multi-colourings of cubic graphs, and conjectures of Fulkerson and Tutte, Proc.
	www.fmf.uni-lj.si /~mohar/Problems/P9BergeFulkersonConjecture.html (223 words)

	VEGA 0.5 Quick Reference Manual: Functions in BLEDE.M (Site not responding. Last check: 2007-10-20)
		Jaws is a cubic graph on 20 vertices.
		Rects is a cubic graph on 14 vertices.
		Ruby is a cubic graph on 18 vertices.
	vega.ijp.si /htmldoc/usages/BLEDE.HTM (114 words)

	Tom's Combinatorial Geometry Class
		By a coloring of a graph we mean an assignment of colors (which we sometimes denote by numbers) to the various parts of the graph, like the vertices, edges, or faces.
		Definition: The chromatic number of a graph G is the fewest number of colors we can use to properly color the vertices of G. This number is denoted X(G).
		A wheel is a graph that consists of a cycle and one vertex in the "middle" which is connected to all the vertices on the cycle.
	www.merrimack.edu /~thull/combgeom/colornotes.html (969 words)

	Math Games: Cubic Symmetric Graphs
		The graph is also symmetric -- any of the ten dominoes could be at the center (try it!).
		Foster Census, which is a listing of all of the cubic symmetric graphs up to 768 vertices.
		In a zero-symmetric graph, the vertices are equivalent, but the edges are maximally dissimilar.
	www.maa.org /editorial/mathgames/mathgames_12_29_03.html (982 words)

	Examples for 5
		1955 is x = 5: the maximum point on the graph is at x = 4.19 which is nearer to 1954; the
		minimum point on the graph is at x = 34.7 which is almost 1985.
		From the graph, the maximum is in approximately 1982.
	www.fiu.edu /~mccoydf/buscal/52prs/52prs.htm (621 words)

	Untitled Document
		A given map can be made cubic by drawing small circles around each vertex with degree greater than 3, and replacing the vertex with the polygon formed by the intersections.
		The number of nodes in a cubic graph is even, since the number of edges (vertices * 3/2) must be an integer.
		Graphs which could not be Tait-colored were called Snarks by Martin Gardner, since like the Lewis Carroll beastie, they were hard to find.
	www.mathpuzzle.com /4Dec2001.htm (6140 words)

	[No title]
		Since the problem of determining whether or not a cubic planar graph has a Hamiltonian circuit is known to be NP-complete [8, 9], this will show that Pearl puzzles are NP-hard.
		For example, the cubic graph on the left in Figure 2 has the rectilinear realization to its right.
		is a cubic graph and the passageways are only one unit wide, a room can not be visited again once the path leaves it.
	www.stetson.edu /~efriedma/papers/pearl/pearl.html (982 words)

	[No title]
		The graph of the basic radical function is EMBED Excel.Chart.8 \s where the domain is all EMBED Equation.DSMT4 and the range is all EMBED Equation.DSMT4 .
		The graph is reflected, because of the negative sign in front of the radical, and shifted up 4 units.
		The graph of a quadratic function is a parabola, with vertex (h, k).
	www2.scc-fl.com /mgoshaw/TextTopic2forMAC2233.doc (2597 words)

	VEGA 0.5 Quick Reference Manual: Functions in BLED.M
		It is assumed that the vertices of vv span a clique in g.
		FromSpecialInvolution[l] constructs a cubic Hamiltonian graph in such a way that the chords are determined by pairs of indices of the form {i,l[[i]]}, for i = 1, 2,..., Length[l].
		SuppressEdge[g,ee] removes the edges form the matching ee in a cubic graph so that the resulting graph remains cubic.
	vega.ijp.si /Htmldoc/usages/BLED.HTM (458 words)

	BBC Education - AS Guru - General Studies - Maths - Functions and Graphs - Polynomial Equations
		You can also solve a quadratic and a linear equation simultaneously by drawing their graphs on the same diagram and finding the co-ordinates of the point or points where they meet.
		If d is positive, the graph goes upwards across the diagram; if d is negative, it goes downwards.
		The graph generally has two places where the gradient is zero (i.e.
	www.bbc.co.uk /education/asguru/generalstudies/maths/12functionsgraphs/functionsgraphs09.shtml (362 words)

	The Parabola And its Roots (Site not responding. Last check: 2007-10-20)
		The graph drawn in the xb-plane has a discontinuity at x = 0.
		The two parts of the graph have vertices at x = 1 and x = -1.
		The same relationship between the three graphs exists as in the case of the parabola.
	jwilson.coe.uga.edu /EMAT6680/Brink/allasgnmts/Graphs3/graphs3.html (427 words)

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