On the Independent Neighborhood Polynomial of the Cartesian Product of Some Special Graphs

Normalah Sharief Abdulcarim, Susan C. Dagondon, Emmy Chacon

Abstract

Two vertices x, y of a graph G are adjacent, or neighbors, if xy is an edge of G. A set S of vertices in a graph G is a neighborhood set if G =[v∈ShN[v]i where hN[v]i is the subgraph induced by v and all the vertices adjacent to v. If no two of the elements of S are adjacent, then S is called an independent neighborhood set. The independent neighborhood polynomial of G of order m is Ni(G, x) = Xm j=ηi(G) ni(G, j)xj where ni(G, j) is the number of independent neighborhood set of G of size j and ηi(G) is the minimum cardinality of an independent neighborhood set of G. This paper investigates the independent neighborhood polynomial of the Cartesian product of some special graphs.

Keywords

Independent Neighborhood Set, Neighborhood Polynomial, Cartesian Product

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