Srivastava, GautamSrivastava, Hari Mohan2024-07-022024-07-022020-02-261578-7303https://doi.org/10.1007/s13398-020-00821-7https://hdl.handle.net/11452/42675A recently defined graph invariant denoted by O(G) for a graph G is shown to have several applications in graph theory. This number gives direct information on the realizability, number of realizations, connectedness, cyclicness, number of components, chords, loops, pendant edges, faces, bridges, etc. In this paper, we use O to give a characterization of connected unicyclic graphs, to calculate the omega invariant and to formalize the number of faces of the line graph of a tree, and give a new algorithm to formalize the independence number of graphs G and line graphs L(G) by means of the support vertices, pendant vertices and isolated vertices in G.eninfo:eu-repo/semantics/closedAccessRealizabilitySequencesCriteriaGraph theoryLine graphsIndependence numberOmega invariantDegree sequenceScience & technologyPhysical sciencesMathematicsMultidisciplinary sciencesMathematicsScience & technology - other topicsArticle000515613100001114210.1007/s13398-020-00821-7