Some Properties of the Lattice of Path Sets of a Connected Graph - R, Girishkumara; S, Lavanya (International Journal of Engineering and Technology, 2018)
It is known that the set of all path sets of a finite connected graph G together with empty set partially ordered by set inclusion relation forms a lattice denoted by PATH(G). In this paper we studied some properties of PATH(G). In fact, it has been shown that an element of PATH(G) is doubly irreducible if and only if it contains a single vertex which is not a cut vertex of G. Also it is proved that PATH(G) is planar if and only if G is a chain of three or more blocks.Â Â