Independence number of graphs and line graphs of trees by means of omega invariant


ÖZDEN AYNA H., Zihni F. E. , Erdogan F., CANGÜL İ. N. , Srivastava G., Srivastava H. M.

REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS, vol.114, no.2, 2020 (Peer-Reviewed Journal) identifier

  • Publication Type: Article / Article
  • Volume: 114 Issue: 2
  • Publication Date: 2020
  • Doi Number: 10.1007/s13398-020-00821-7
  • Journal Name: REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS
  • Journal Indexes: Science Citation Index Expanded, Scopus, Aerospace Database, Communication Abstracts, MathSciNet, zbMATH, DIALNET, Civil Engineering Abstracts

Abstract

A 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.