Results 61 to 70 of about 568,566 (214)
A Categorification for the Signed Chromatic Polynomial
The Electronic Journal of Combinatorics, 2022 By coloring a signed graph by signed colors, one obtains the signed chromatic polynomial of the signed graph. For each signed graph we construct graded cohomology groups whose graded Euler characteristic yields the signed chromatic polynomial of the signed graph.
Zhiyun Cheng +3 more
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Entropy and Multi-Fractal Analysis in Complex Fractal Systems Using Graph Theory
Axioms, 2023 In 1997, Sierpinski graphs, S(n,k), were obtained by Klavzar and Milutinovic. The graph S(1,k) represents the complete graph Kk and S(n,3) is known as the graph of the Tower of Hanoi. Through generalizing the notion of a Sierpinski graph, a graph named a
Zeeshan Saleem Mufti +3 more
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The chromatic polynomials of signed Petersen graphs [PDF]
, 2013 Zaslavsky proved in 2012 that, up to switching isomorphism, there are six different signed Petersen graphs and that they could be told apart by their chromatic polynomials, by showing that the latter give distinct results when evaluated at 3.
M. Beck +4 more
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Approximating the Chromatic Polynomial
CoRR, 2016 Chromatic polynomials are important objects in graph theory and statistical physics, but as a result of computational difficulties, their study is limited to graphs that are small, highly structured, or very sparse. We have devised and implemented two algorithms that approximate the coefficients of the chromatic polynomial $P(G,x)$, where $P(G,k)$ is ...
Yvonne Kemper, Isabel Beichl
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Fuzzy Chromatic Polynomial of Fuzzy Graphs with Crisp and Fuzzy Vertices Using α-Cuts
Advances in Fuzzy Systems, 2019 Coloring of fuzzy graphs has many real life applications in combinatorial optimization problems like traffic light system, exam scheduling, register allocation, etc.
Mamo Abebe Ashebo +1 more
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Modifications of Tutte–Grothendieck invariants and Tutte polynomials
AKCE International Journal of Graphs and Combinatorics, 2020 Generalized Tutte–Grothendieck invariants are mappings from the class of matroids to a commutative ring that are characterized recursively by contraction–deletion rules. Well known examples are Tutte, chromatic, tension and flow polynomials.
Martin Kochol
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Chromatic polynomials of graphs from Kac–Moody algebras [PDF]
, 2013 We give a new interpretation of the chromatic polynomial of a simple graph $$G$$G in terms of the Kac–Moody Lie algebra $$\mathfrak {g}$$g with Dynkin diagram $$G$$G.
R. Venkatesh, S. Viswanath
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Algebraic methods for chromatic polynomials [PDF]
, 2003 The chromatic polynomials of certain families of graphs can be calculated by a transfer matrix method. The transfer matrix commutes with an action of the symmetric group on the colours.
Reinfeld, Philipp Augustin
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Discrete Mathematics, 1994 Let \(T_ G(\lambda)\) denote the number of \(T\)-colourings of graph \(G\) of order \(n\). The author shows that for each set \(T\) of nonnegative integers with maximal element \(r\), there is a polynomial \(Q_ G(\lambda)\) such that \(Q_ G(\lambda)= T_ G(\lambda)\) for all \(\lambda\geq r(n- 1)\).
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On the Roots of Chromatic Polynomials
Journal of Combinatorial Theory, Series B, 1998 A 2-tree is a graph constructed from \(K_2\) by successively joining a new vertex to both vertices of an existing edge. The author shows the following: (1) The chromatic polynomial of a connected graph with \(n\) vertices and \(m\) edges has a root with modulus at least \((m-1)/(n- 2)\).
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