The Nullity of Identifying Path Graph with Some Special Graphs

Payman A. Rashed

Dep. of Mathematics, College of Basic Education,University of Salahaddin, Erbil, Iraq

DOI: https://doi.org/10.17656/jzs.10622

Original: 16 July 2016, Revised: 5 November 2016, Accepted: 20 November 2016, Published online: 20 June 2017

Abstract

In this paper the idea of high zero-sum weighting of new technique is used to find the nullity of some special graphs Gp, Gk, Gc which are constructed by identifying the path graph pn of different order with star graph, complete graph, and cycle graph ,pn S1,m, pn Kp and pn cm, respectively. And it is proved that the nullity of these new graphs is increases or decreases according to the changing of identifying vertex in the path, or the other graphs, and with the order of path which is even or odd.

Key Words: Path graph, identifying graphs, The nullity of a graph.

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