2-Domination Polynomial of Tensor Product of Paths

We have calculated the 2-domination number of the tensor product of P2 and Pn. We have derived the distance-2 domination polynomials of tensor product of P2 and Pn

Connected Hub Sets and Connected Hub Polynomials of the Lollipop Graph L_(p,1)

Let  be a graph with vertex set . The number of vertices in  is the order of  and is denoted by . The connected hub polynomial of Gdenoted by  is defined as  where  denotes the number of connected hub sets of  of cardinality and denotes the connected hub number of .Let  denotes the Lollipop graph with  vertices. The connected hub polynomial of  denoted by  is defined as,where denotes the number of connected hub sets of  of cardinality , and denotes the connected hub number of .In this paper, we derive a recursive formula for . From this recursive formula, we construct the connected hub polynomial of  as,Also we study some properties of this polynomia

On the monophonic and monophonic domination polynomial of a graph

A set S of vertices of a graph G is a monophonic set of G if each vertex u of G lies on an u − v monophonic path in G for some u, v ∈ S. M ⊆ V (G) is said to be a monophonic dominating set if it is both a monophonic set and a dominating set. Let M(G, i) be the family of monophonic sets of a graph G with cardinality i and let m(G, i) = |M(G, i)|. Then the monophonic polynomial M(G, x) of G is defined as M(G, x) = Ʃⁿi=m(G) m(G, i)xⁱ, where m(G) is the monophonic number of G. In this article, we have introduced monophonic domination polynomial of a graph. We have computed the monophonic and monophonic domination polynomials of some specific graphs. In addition, monophonic and monophonic domination polynomial of the Corona product of two graphs is derived.Publisher's Versio

On the strong dominating sets of graphs

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