Connected Domination Polynomial of Some Graphs

Abstract

Let G be a simple connected graph. The connected domination polynomial of G is defined by

On Total Domination Polynomials of Certain Graphs

“…Proof: Let G be a path P 7 with the vertex set {1, 2, 3, 4, 5, 6, 7} and let H be the sub graph P 6 with the vertex set {1, 2, 3, 4, 5, 6} of P 7 .…”

“…We have introduced the total domination polynomial for any simple non isolated graph G in [7] and is defined by…”

“…In [7] We have obtained some properties of D t (G, x) and its coefficients. Also, we have calculated the total domination polynomials of complete graph, complete bipartite graph, join of two graphs and a graph consisting of disjoint components.…”

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Abstract:We have introduced the total domination polynomial for any simple non isolated graph G in [7] and is defined byis the cardinality of total dominating sets of G of size i, and γ t (G) is the total domination number of G.In [7] We have obtained some properties of D t (G, x) and its coefficients. Also, we have calculated the total domination polynomials of complete graph, complete bipartite graph, join of two graphs and a graph consisting of disjoint components.

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