EULERIAN AND HAMILTONIAN PROPERTIES OF GALLAI AND ANTI-GALLAI TOTAL GRAPHS - Pravin Garg; Deepa Sinha; Shanu Goyal (IndoMS, 2015)
Let G = (V, E) be a graph. The Gallai total graph Γ_T(G) of G is the graph, where V(Γ_T(G))=V E and uv E(Γ_T(G)) if and only if itemize [(i)] u and v are adjacent vertices in G, or [(ii)] u is incident to v or v is incident to u in G, or [(iii)] u and v are adjacent edges in G which do not span a triangle in G. itemize The anti-Gallai total graph Δ_T(G) of G is the graph, where V(Δ_T(G))=V E and uv E(Δ_T(G)) if and only if itemize [(i)] u and v are adjacent vertices in G, or [(ii)] u is incident to v or v is incident to u in G, or [(iii)] u and v are adjacent edges in G and lie on a same triangle in G. itemize In this paper, we discuss Eulerian and Hamiltonian properties of Gallai and anti-Gallai total graphs.DOI : http://dx.doi.org/10.22342/jims.21.2.230.105-116