ON THE TRAVERSABILITY OF NEW COMPOSITION OF TOTAL GRAPHS

ON THE TRAVERSABILITY OF NEW COMPOSITION OF TOTAL GRAPHS

S. Goyal, Tanya

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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 ΔT (G). In this paper, we study the Eulerian and Hamiltonian properties of the resulting graphs.

Keywords

Euler graph, Hamiltonian graph, composition of two graphs, Gallai total graph, anti-Gallai total graph.