The path graph of the amalgamated graph of C3 and Cn at an edge or at a vertex

Abstract

Path graphs were proposed as a generalization of line graphs.  The 2-path graph denoted by P₂(G), of a graph G has vertex set the set of all paths of length two.  Two such vertices are adjacent in the new graph if their union is a path of length three or a cycle of length three.  In this paper we will introduce the path graph of the amalgamated graph of C₃ and C_n at an edge and at a vertex.  Also, some new properties of these graphs will be given such as the independence number, domination number and matching number.