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, cilt.114, sa.2, 2020 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 114 Sayı: 2
  • Basım Tarihi: 2020
  • Doi Numarası: 10.1007/s13398-020-00821-7
  • Dergi Adı: REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, Communication Abstracts, MathSciNet, zbMATH, DIALNET, Civil Engineering Abstracts
  • Anahtar Kelimeler: Graph theory, Line graphs, Independence number, Omega invariant, Degree sequence, REALIZABILITY, SEQUENCES, CRITERIA
  • Bursa Uludağ Üniversitesi Adresli: Evet

Özet

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.