Properties of Strong Double Graphs
T. A. Chishti, Hilal A. Ganie, S. Pirzada · Journal of Discrete Mathematical Sciences and Cryptography · 2014
For a graph G with vertex set V(G) = {v1, v2, ···, vn}, the strong double graph SD(G) is a graph obtained by taking two copies of G and joining each vertex vi in one copy with the closed neighbourhood N[vi] = N(vi), {vi} of corresponding vertex in another copy. In this paper, we study some basic properties of being bipartite, Hamiltonian and strongly regular of the graph SD(G). We also obtain the chromatic number of SD(G). We have a formula for the number of spanning trees of SD(G) in terms of the number of spanning trees of G.