Abstract

Abstract: Let G be a graph and E1 ⊂ E(G). A Smarandachely E1-lict graph nE1(G) of a graph G is the graph whose point set is the union of the set of lines in E1 and the set of cutpoints of G in which two points are adjacent if and only if the corresponding lines of G are adjacent or the corresponding members of G are incident.Here the lines and cutpoints of G are member of G. Particularly, if E1 = E(G), a Smarandachely E(G)-lict graph nE(G)(G) is abbreviated to lict graph of G and denoted by n(G). In this paper, the concept of pathos lict sub-division graph Pn[S(T)] is introduced. Its study is concentrated only on trees. We present a characterization of those graphs, whose lict sub-division graph is planar, outerplanar, maximal outerplanar and minimally nonouterplanar. Further, we also establish the characterization for Pn[S(T)] to be eulerian and hamiltonian. Key Words: pathos, path number, Smarandachely lict graph, lict graph, pathos lict sub-division graphs, Smarandache path k-cover, pathos point.