On the traversability of near common neighborhood graph of a graph

Abstract

The near common neighborhood graph of a graph G, denoted by
ncn(G) is defined as the graph on the same vertices of G, two vertices
are adjacent in ncn(G), if there is at least one vertex in G not adjacent
to both the vertices. In this research paper, the conditions for ncn(G)
to be disconnected are discussed and also we present characterization
for graph ncn(G) to be hamiltonian and eulerian.