On pathos block line graph of a tree

Abstract

Let T be a tree of order n ≥ 2. A pathos line graph of T, written PL(T), is a graph whose vertices are the edges and paths of a pathos of T, with two vertices of PL(T) adjacent whenever the corresponding edges of T are adjacent or the edge lies on the corresponding path of the pathos. An extension is called a pathos block line graph, denoted by PBL(T), and is similar to PL(T), except that the adjacency of pathos vertices. For this class of graphs we discuss the planarity, outer planarity, maximal outer planarity, minimally nonouter planarity, and crossing number one properties of these graphs.