Results 11 to 20 of about 2,394 (219)
Application of maple on computing strong fuzzy chromatic polynomial of fuzzy graphs [PDF]
BMC Research Notes, 2022 Objective In the field of graph theory, maple is a technical computation form that is used for solving problems. In this article, we apply maple to find the strong fuzzy chromatic polynomial of fuzzy graphs and related. Moreover, we apply maple to obtain
Mamo Abebe Ashebo +2 more
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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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Boundary Chromatic Polynomial [PDF]
Journal of Statistical Physics, 2008 We consider proper colorings of planar graphs embedded in the annulus, such that vertices on one rim can take Q_s colors, while all remaining vertices can take Q colors. The corresponding chromatic polynomial is related to the partition function of a boundary loop model. Using results for the latter, the phase diagram of the coloring problem (with real
Jacobsen, Jesper Lykke, Saleur, Hubert
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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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A chromatic partition polynomial
Discrete Mathematics, 1998 Let \(|\pi|\) denote the number of blocks in a partition \(\pi\) of \([n]= \{1,2, \dots, n\}\). Let \(p=a_1 a_2 \dots a_n\) be a permutation of \([n]\). A descent block of \(p\) is a maximal decreasing continuance subword \(a_ia_{i+1} \dots a_j\) of \(p\). The \(n\)th Eulerian polynomial \(A_n(t)\) (for \(n=0,1,2,\dots)\) is defined by \[ \sum_{k\geq 0}
Steingrímsson, Einar +1 more
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Maximum chromatic polynomial of 3-chromatic blocks
Discrete Mathematics, 1997 This article continues the work done by the author in [Maximum chromatic polynomials of 2-connected graphs, J. Graph Theory 18, No. 4, 329-336 (1994; Zbl 0809.05046)]. In that paper it was shown that the 2-connected graph of order \(n\) with the greatest number \(P(G,3)\) of proper 3-colourings is \(C_n\) (and, for \(n=5\), \(K_{2,3}\)), and that \(K_ ...
Tomescu, Ioan
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On the Absolute Sum of Chromatic Polynomial Coefficient of Graphs [PDF]
International Journal of Mathematics and Mathematical Sciences, 2011 The absolute sum of chromatic polynomial coefficient of forest, q-tree, unicyclic graphs, and quasiwheel graphs, are determined in this paper.
Shubo Chen
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Two Chromatic Polynomial Conjectures
Journal of Combinatorial Theory, Series B, 1997 Let \(P(t)\) be the chromatic polynomial of a graph. It is shown that \(P(5)^{-1}P(6)^2 P(7)^{-1}\) can be arbitrarily small, disproving a conjecture of Welsh that \(P(t)^2\geq P(t- 1)P(t+1)\), and also disproving several other conjectures of Brenti.
Seymour, Paul
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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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