ON THE GENERALIZED abc - BLOCK EDGE TRANSFORMATION GRAPHS
B. BASAVANAGOUD*, KEERTHI G. MIRAJKAR, POOJA B, Shreekant Patil · International Journal of Mathematical Archive · 2017
Given a graph with vertex set , edge set and block set , let be the complement, the line graph and the block graph of . Let be the graph with and with no edges, the complete graph with , , and . Let be the graph whose vertices can be put in one to one correspondence with the set of edges and blocks of G in such a way that two vertices of are adjacent if and only if one corresponds to a block of and the other to an edge of and is in (resp., is not in) . Given the abc - block edge transformation graph of is the graph with vertex set and the edge set where if , if , is the graph with and with no edges if , is the complete bipartite graph with parts and if . In this paper, we investigate some basic properties such as order, size, vertex degree and connectedness of the these generalized abc - block edge transformation graphs .