Recurrence Relations and Splitting Formulas for the Domination Polynomial
نویسندگان
چکیده
منابع مشابه
Recurrence Relations and Splitting Formulas for the Domination Polynomial
The domination polynomial D(G, x) of a graph G is the generating function of its dominating sets. We prove that D(G, x) satisfies a wide range of reduction formulas. We show linear recurrence relations for D(G, x) for arbitrary graphs and for various special cases. We give splitting formulas for D(G, x) based on articulation vertices, and more generally, on splitting sets of vertices.
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15 صفحه اولDomination in Degree Splitting Graphs
Let G = (V, E) be a graph with V = S1 S2 ...,St T where each Si is a set of vertices having at least two vertices and having the same degree and T = V Si. The degree splitting graph of G is denoted by DS(G) is obtained from G by adding vertices w1, w2, ..., wt and joining wi to each vertex of Si (1 i t). Let the vertices and the edges of a graph G are called the elements of G. In this...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2012
ISSN: 1077-8926
DOI: 10.37236/2475