초록
A pathos block line cut-vertex graph of a tree T, written P BLc(T), is a graph whose vertices are the blocks, cut-vertices, and paths of a pathos of T, with two vertices of P BLc(T) adjacent whenever the corresponding blocks of T have a vertex in common or the edge lies on the corresponding path of the pathos or one corresponds to a block Bi of T and the other corresponds to a cut-vertex cj of T such that cj is in Bi; two distinct pathos vertices Pm and Pn of P BLc(T) are adjacent whenever the corresponding paths of the pathos Pm(vi, vj) and Pn(vk, vl) have a common vertex. We study the properties of P BLc(T) and present the characterization of graphs whose P BLc(T) are planar; outerplanar; maximal outerplanar; minimally nonouterplanar; eulerian; and hamiltonian. We further show that for any tree T, the crossing number of P BLc(T) can never be one.