Characterization of total line-cut graphs

Abstract

The total line-cut graph of a graph G = (V,E), denoted by TL_c(G), is the graph with point set E(G) ∪ W(G), where W(G) is the set of cutpoints of G, in which two points are adjacent if and only if they correspond to adjacent lines of G or correspond to adjacent or coadjacent cutpoints of G or one point corresponds to a line e of G and the other corresponds to a cutpoint c of G such that e is incident with c. In this paper, we offer a structural characterization of total line-cut graphs.