Results 21 to 30 of about 1,320 (180)
Burnside Chromatic Polynomials of Group-Invariant Graphs
Discussiones Mathematicae Graph Theory, 2023 We introduce the Burnside chromatic polynomial of a graph that is invariant under a group action. This is a generalization of the Q-chromatic function Zaslavsky introduced for gain graphs.
White Jacob A.
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On the degree-chromatic polynomial of a tree [PDF]
Discrete Mathematics & Theoretical Computer Science, 2012 The degree chromatic polynomial $P_m(G,k)$ of a graph $G$ counts the number of $k$ -colorings in which no vertex has m adjacent vertices of its same color.
Diego Cifuentes
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Connection between Graphs' Chromatic and Ehrhart Polynomials [PDF]
Journal of Applied Sciences and Nanotechnology, 2023 Graph Theory is a discipline of mathematics with numerous outstanding issues and applications in a variety of sectors of mathematics and science. The chromatic polynomial is a type of polynomial that has useful and attractive qualities.
Ola Neamah, Shatha Salman
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Recursion Relations for Chromatic Coefficients for Graphs and Hypergraphs
Discussiones Mathematicae Graph Theory, 2022 We establish a set of recursion relations for the coefficients in the chromatic polynomial of a graph or a hypergraph. As an application we provide a generalization of Whitney’s broken cycle theorem for hypergraphs, as well as deriving an explicit ...
Durhuus Bergfinnur, Lucia Angelo
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The Amazing Chromatic Polynomial [PDF]
The Mathematical Intelligencer, 2022 17 pages, 8 ...
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Chromatic Polynomial of Intuitionistic Fuzzy Graphs Using α,β-Levels
International Journal of Mathematics and Mathematical Sciences, 2022 The article describes a new thought on the chromatic polynomial of an intuitionistic fuzzy graph which is illustrated based on α,β-level graphs. Besides, the alpha-beta fundamental set of an intuitionistic fuzzy graph is also defined with a vivid ...
V. N. SrinivasaRao Repalle +2 more
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The game chromatic number of trees and forests [PDF]
Discrete Mathematics & Theoretical Computer Science, 2015 While the game chromatic number of a forest is known to be at most 4, no simple criteria are known for determining the game chromatic number of a forest. We first state necessary and sufficient conditions for forests with game chromatic number 2 and then
Charles Dunn +4 more
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Chromatic polynomials of hypergraphs
Applied Mathematics Letters, 2007 The authors investigate the number of \(\lambda\)-colourings of the vertices of a hypergraph \(H\) such that each edge \(e_i\) of \(H\) contains at least \(x_i\) differently coloured vertices for given quantities \(x_1,\dots,x_m\) (one for each edge).
Ewa Drgas-Burchardt, Ewa Lazuka
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Chromatic Polynomials of Signed Book Graphs
Theory and Applications of Graphs, 2022 For $m \geq 3$ and $n \geq 1$, the $m$-cycle \textit{book graph} $B(m,n)$ consists of $n$ copies of the cycle $C_m$ with one common edge. In this paper, we prove that (a) the number of switching non-isomorphic signed $B(m,n)$ is $n+1$, and (b) the ...
Deepak Sehrawat, Bikash Bhattacharjya
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Short certificates for chromatic equivalence
Journal of Graph Algorithms and Applications, 2019 The chromatic polynomial gives the number of proper colourings of a graph in terms of the number of available colours. In general, calculating chromatic polynomials is #P-hard.
Zoe Bukovac, Graham Farr, Kerri Morgan
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