Results 31 to 40 of about 4,659 (167)
Vertex-weighted Wiener polynomials of subdivision-related graphs [PDF]
Opuscula Mathematica, 2016 Singly and doubly vertex-weighted Wiener polynomials are generalizations of both vertex-weighted Wiener numbers and the ordinary Wiener polynomial. In this paper, we show how the vertex-weighted Wiener polynomials of a graph change with subdivision ...
Mahdieh Azari +2 more
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Polynomial hulls of graphs [PDF]
Pacific Journal of Mathematics, 1991 We consider the polynomially convex hull of the graph of a continuous complex-valued function on the boundary of the unit ball. We show first that the hull covers the closed unit ball and then consider several of its properties. In particular, when is the hull also a graph; i.e. single sheeted?
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Interlace polynomials of friendship graphs
Electronic Journal of Graph Theory and Applications, 2018 In this paper, we study the interlace polynomials of friendship graphs, that is, graphs that satisfy the Friendship Theorem given by Erdös, Rényi and Sos.
Christina Eubanks-Turner, Aihua Li
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On Topological Indices of Total Graph and Its Line Graph for Kragujevac Tree Networks
Complexity, 2021 Kragujevac tree is indicated by K; K∈Kgq=s2t+1+1,s with order and size s2t+1+1 and s2t+1, respectively. In this paper, we have a look at certain topological features of the total graph and line graph of the total graph of the considered tree, i.e ...
Salma Kanwal +6 more
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The construction of graphs with irreducible matching polynomials and their generalizations
AKCE International Journal of Graphs and CombinatoricsThis paper investigates methods for constructing graphs whose matching polynomials are irreducible over [Formula: see text]. Building on this, the construction method is extended to general graph polynomials, for graphs whose polynomials satisfy certain ...
Hou Shengzhe
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On the dependence polynomial of a graph
European Journal of Combinatorics, 2007 For an \(n\)-vertex graph \(G\) and \(i=0, 1, \dots, n\), let \(c_i\) denote the number of complete subgraphs on \(i\) vertices in \(G\). The dependence polynomial \(P_G(z)\) of \(G\) is defined by \(P_G(z)=1+\sum_{i=1}^n (-1)^i c_iz^i\). Using a Möbius-type inversion formula, the authors show that \[ \begin{aligned} P_G(z)&=\sum_{\emptyset\not ...
Jianguo Qian, Andreas Dress, Yan Wang
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The chromatic polynomial of a graph [PDF]
Pacific Journal of Mathematics, 1985 First, the author summarizes some known results on chromatical polynomials and sketches their proofs. Then he lists the chromatical polynomials of all graphs with fewer than seven vertices.
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RC-Graphs and Schubert Polynomials [PDF]
Experimental Mathematics, 1993 Using a formula of Billey, Jockusch and Stanley, Fomin and Kirillov have introduced a new set of diagrams that encode the Schubert polynomials. We call these objects rc-graphs. We define and prove two variants of an algorithm for constructing the set of all rc-graphs for a given permutation.
Nantel Bergeron, Sara C. Billey
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Independent set-based multivariate graph polynomials for fractal-type silicate triangle structures
Frontiers in ChemistrySilicate structures are the mineral materials widely studied for their extraordinary structural complexity and versatility. They naturally exhibit self-similarity, making them well-suited for analysis through chemical graphs, graph polynomials, and ...
K. S. Nithiya, D. Easwaramoorthy
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A Homomorphic Polynomial for Oriented Graphs
The Electronic Journal of Combinatorics, 2023 In this article, we define a function that counts the number of (onto) homomorphisms of an oriented graph. We show that this function is always a polynomial and establish it as an extension of the notion of chromatic polynomials. We study algebraic properties of this function.
Sandip Das 0001 +3 more
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