Laceability in the Image Graph of Some Classes of Graphs

Abstract

A connected graph G is termed Hamiltonian-t-laceable (Hamiltonian-t*-laceable) if there exists in it a Hamiltonian path between every pair (at least one pair) of distinct vertices u and v with the property d(u,v) = t, 1 \(\le\) t \(\le\) diamG.  In [1] the authors Vaidya and Bijukumar defined the joint sum of the cycle C_n as follows. Consider two copies of C_n, connect a vertex of the first copy to a vertex of the second copy with a new edge. The new graph obtained is called joint sum of C_n . Another type of graph called the double graph of a graph is constructed by taking two copies of G and adding edges u₁v₂ and v₂u₁ for every edge uv of G.  The image graph of a connected graph G, denoted by I_mg (G) , is the graph obtained by joining the vertices of the original graph G to the corresponding vertices of a copy of G. We investigate the laceability properties of the image graph of some classes of graphs in this chapter.