A multivariate interlace polynomial and its computation for graphs of bounded clique-width.
Courcelle, Bruno (2008)
The Electronic Journal of Combinatorics [electronic only]
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Courcelle, Bruno (2008)
The Electronic Journal of Combinatorics [electronic only]
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Beezer, Robert A., Farrell, E.J. (2000)
International Journal of Mathematics and Mathematical Sciences
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Reza Jafarpour-Golzari (2022)
Commentationes Mathematicae Universitatis Carolinae
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We introduce a new concept namely the degree polynomial for the vertices of a simple graph. This notion leads to a concept, namely, the degree polynomial sequence which is stronger than the concept of degree sequence. After obtaining the degree polynomial sequence for some well-known graphs, we prove a theorem which gives a necessary condition for the realizability of a sequence of polynomials with positive integer coefficients. Also we calculate the degree polynomial for the vertices...
Farrell, E.J. (1989)
International Journal of Mathematics and Mathematical Sciences
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Hagos, Elias M. (2000)
The Electronic Journal of Combinatorics [electronic only]
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Li, Xueliang, Gutman, Ivan, Milovanović, V.Gradimir (2000)
Publications de l'Institut Mathématique. Nouvelle Série
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Farrell, E.J. (1981)
International Journal of Mathematics and Mathematical Sciences
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Araujo, Oswaldo, Estrada, Mario, Morales, Daniel A., Rada, Juan (2005)
International Journal of Mathematics and Mathematical Sciences
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I. Gutman (1978)
Publications de l'Institut Mathématique [Elektronische Ressource]
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Gutman, Ivan (1992)
Publications de l'Institut Mathématique. Nouvelle Série
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I. Gutman, Olga Miljković, B. Zhou, M. Petrović (2006)
Bulletin, Classe des Sciences Mathématiques et Naturelles, Sciences mathématiques
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Ivan Gutman (1977)
Publications de l'Institut Mathématique
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Markus Dod, Tomer Kotek, James Preen, Peter Tittmann (2015)
Discussiones Mathematicae Graph Theory
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This paper introduces a trivariate graph polynomial that is a common generalization of the domination polynomial, the Ising polynomial, the matching polynomial, and the cut polynomial of a graph. This new graph polynomial, called the bipartition polynomial, permits a variety of interesting representations, for instance as a sum ranging over all spanning forests. As a consequence, the bipartition polynomial is a powerful tool for proving properties of other graph polynomials and graph...
Matchett, Philip (2004)
The Electronic Journal of Combinatorics [electronic only]
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Ashrafi, A., Ghorbani, M., Hossein-Zadeh, M. (2011)
Serdica Journal of Computing
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The eccentric connectivity index of a graph G, ξ^C, was proposed by Sharma, Goswami and Madan. It is defined as ξ^C(G) = ∑ u ∈ V(G) degG(u)εG(u), where degG(u) denotes the degree of the vertex x in G and εG(u) = Max{d(u, x) | x ∈ V (G)}. The eccentric connectivity polynomial is a polynomial version of this topological index. In this paper, exact formulas for the eccentric connectivity polynomial of Cartesian product, symmetric difference, disjunction and join of graphs are presented. ...