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

Authors

  • Normalah Sharief Abdulcarim Mindanao State University Main Campus, Marawi City
  • Susan C. Dagondon Mindanao State University-Iligan Institute of Technology
  • Emmy Chacon Mindanao State University-Iligan Institute of Technology

DOI:

https://doi.org/10.29020/nybg.ejpam.v14i1.3860

Keywords:

Independent Neighborhood Set, Neighborhood Polynomial, Cartesian Product

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.

Author Biographies

  • Normalah Sharief Abdulcarim, Mindanao State University Main Campus, Marawi City
    Department of Mathematics
  • Susan C. Dagondon, Mindanao State University-Iligan Institute of Technology
    Department of Mathematics
  • Emmy Chacon, Mindanao State University-Iligan Institute of Technology
    Department of Mathematics

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Published

2021-01-31

Issue

Vol. 14 No. 1: (January 2021)

Section

Nonlinear Analysis

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How to Cite

On the Independent Neighborhood Polynomial of the Cartesian Product of Some Special Graphs. (2021). European Journal of Pure and Applied Mathematics, 14(1), 173-191. https://doi.org/10.29020/nybg.ejpam.v14i1.3860