The graph polynomial and the number of proper vertex coloring

Michael Tarsi

Displaying similar documents to “The graph polynomial and the number of proper vertex coloring”

Antisymmetric flows and strong colourings of oriented graphs

J. Nešetřill, André Raspaud (1999)

Annales de l'institut Fourier

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The homomorphisms of oriented or undirected graphs, the oriented chromatic number, the relationship between acyclic colouring number and oriented chromatic number, have been recently intensely studied. For the purpose of duality, we define the notions of strong-oriented colouring and antisymmetric-flow. An antisymmetric-flow is a flow with values in an additive abelian group which uses no opposite elements of the group. We prove that the strong-oriented chromatic number ${\vec{χ}}_{s}$ (as the modular...

The Acyclic Polynomial Of A Graph

Ivan Gutman (1977)

Publications de l'Institut Mathématique

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Glossary of signed and gain graphs and allied areas.

Zaslavsky, Thomas (1998)

The Electronic Journal of Combinatorics [electronic only]

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A small trivalent graph of girth 14.

Exoo, Geoffrey (2002)

The Electronic Journal of Combinatorics [electronic only]

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Colouring the petals of a graph.

Cariolaro, David, Cariolaro, Gianfranco (2003)

The Electronic Journal of Combinatorics [electronic only]

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The edge C₄ graph of some graph classes

Manju K. Menon, A. Vijayakumar (2010)

Discussiones Mathematicae Graph Theory

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The edge C₄ graph of a graph G, E₄(G) is a graph whose vertices are the edges of G and two vertices in E₄(G) are adjacent if the corresponding edges in G are either incident or are opposite edges of some C₄. In this paper, we show that there exist infinitely many pairs of non isomorphic graphs whose edge C₄ graphs are isomorphic. We study the relationship between the diameter, radius and domination number of G and those of E₄(G). It is shown that for any graph G without isolated vertices,...

A generalization of the dichromatic polynomial of a graph.

Farrell, E.J. (1981)

International Journal of Mathematics and Mathematical Sciences

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Functigraphs: An extension of permutation graphs

Andrew Chen, Daniela Ferrero, Ralucca Gera, Eunjeong Yi (2011)

Mathematica Bohemica

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Let $G_{1}$ and $G_{2}$ be copies of a graph $G$ , and let $f : V (G_{1}) \to V (G_{2})$ be a function. Then a functigraph $C (G, f) = (V, E)$ is a generalization of a permutation graph, where $V = V (G_{1}) \cup V (G_{2})$ and $E = E (G_{1}) \cup E (G_{2}) \cup {u v : u \in V (G_{1}), v \in V (G_{2}), v = f (u)}$ . In this paper, we study colorability and planarity of functigraphs.