On the traversability of new composition of total graphs

Abstract

The F-composition F(G)[H] is a graph with the set of vertices V (F(G)[H]) = (V (G) ∪ E(G)) × V (H) and two vertices u = (u1, u2) and v = (v1, v2) of F(G)[H] are adjacent if and only if [u1 = v1 ∈ V (G) and (u2, v2) ∈ E(H)] or [(u1, v1) ∈ E(F(G))]. Here F(G) be one of the symbols ΓT (G), or ∆T (G). In this paper, we study the Eulerian and Hamiltonian properties of the resulting graphs.