Results 21 to 30 of about 7,067 (209)
The cycle (circuit) polynomial of a graph with double and triple weights of edges and cycles
Electronic Journal of Graph Theory and Applications, 2019 Farrell introduced the general class of graph polynomials which he called the family polynomials, or F-polynomials, of graphs. One of these is the cycle, or circuit, polynomial.
Vladimir R. Rosenfeld
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Discrete Applied Mathematics, 1992 For directed graphs \(G=(V_ G,E_ G)\) and \(H=(V_ H,E_ H)\) an \(H\)- coloring of \(G\) is a mapping \(f:V_ G\to V_ H\) such that for all edges \((u,v)\in E_ G\) we have \((f(u),f(v))\in E_ H\). The authors introduce a new technique for proving that the \(H\)-coloring problem is polynomially solvable for some fixed digraphs \(H\).
Gutjahr, W., Welzl, E., Woeginger, G.J.
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Computing Wiener and Hyper-Wiener Indices of Zero-Divisor Graph of ℤℊ3×ℤI1I2
Journal of Function Spaces, 2022 Let S=ℤℊ3×ℤI1I2 be a commutative ring where ℊ,I1 and I2 are positive prime integers with I1≠I2. The zero-divisor graph assigned to S is an undirected graph, denoted as YS with vertex set V(Y(S)) consisting of all Zero-divisor of the ring S and for any c,
Yonghong Liu +4 more
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Design of quadrature rules for Müntz and Müntz-logarithmic polynomials using monomial transformation [PDF]
, 2009 A method for constructing the exact quadratures for Müntz and Müntz-logarithmic polynomials is presented. The algorithm does permit to anticipate the precision (machine precision) of the numerical integration of Müntz-logarithmic polynomials in terms of ...
Lombardi, Guido
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A Note on Graph Colorings and Graph Polynomials
Journal of Combinatorial Theory, Series B, 1997 Given a graph \(G\), form a polynomial \(\prod (x_i-x_j)\) where the product is over all edges \((i,j)\) with \(i < j\). If \(G\) is not \(k\)-colourable, then no matter how the variables \(x_i\) are assigned integers from \(1\) to \(k\) the polynomial is zero. Hence the graph polynomial encodes chromatic properties of the graph.
Noga Alon, Michael Tarsi
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CoRR, 2018 We study the time complexity of induced subgraph isomorphism problems where the pattern graph is fixed. The earliest known example of an improvement over trivial algorithms is by Itai and Rodeh (1978) who sped up triangle detection in graphs using fast matrix multiplication.
Markus Bläser +2 more
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A novel approach for the system of coupled differential equations using clique polynomials of graph
Partial Differential Equations in Applied Mathematics, 2022 This study proposed an efficient numerical technique for coupled differential equations (CDEs) using the clique polynomials of the Complete graph. Recently, Graph theory has dragged the attention of many mathematicians due to its wide applications. Here,
Kumbinarasaiah S., Manohara G.
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Evaluations of Graph Polynomials [PDF]
, 2008 A graph polynomial $p(G, \bar{X})$ can code numeric information about the underlying graph G in various ways: as its degree, as one of its specific coefficients or as evaluations at specific points $\bar{X}= \bar{x}_0$. In this paper we study the question how to prove that a given graph parameter, say *** (G ), the size of the maximal clique of G ...
Benny Godlin +2 more
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On coefficients of circuit polynomials and characteristic polynomials
International Journal of Mathematics and Mathematical Sciences, 1985 Results are given from which expressions for the coefficients of the simple circuit polynomial of a graph can be obtained in terms of subgraphs of the graph. From these are deduced parallel results for the coefficients of the characteristic polynomial of
E. J. Farrell
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Omega, Sadhana, and PI Polynomials of Quasi-Hexagonal Benzenoid Chain
Journal of Analytical Methods in Chemistry, 2020 Counting polynomials are important graph invariants whose coefficients and exponents are related to different properties of chemical graphs. Three closely related polynomials, i.e., Omega, Sadhana, and PI polynomials, dependent upon the equidistant edges
Nazeran Idrees +5 more
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