Omega invariant of the line graphs of unicyclic graphs

Abstract

A recently introduced graph invariant Ω(G) for a graph G is proven to have several nice applications in Graph Theory and Com-binatorics. This number gives direct information on the number of components, realizability, cyclicness, connectedness, chords, loops, pendant edges, faces, bridges and the number of realizations. In this paper, we determine Ω values of the line graphs of unicyclic graphs.