• ON THE GENERALIZED abc - BLOCK EDGE TRANSFORMATION GRAPHS

Abstract

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 .