Title: Omega Invariant of the Line Graphs of Unicyclic Graphs
Montes Taurus J. Pure Appl. Math. / ISSN: 2687-4814
Article ID: MTJPAM-D-19-00014; Volume 2 / Issue 2 / Year 2020, Pages 45-48
Document Type: Research Paper
Author(s): Muge Togan a , Aysun Yurttas Gunes b , Sadik Delen c , Ismail Naci Cangul d
aFaculty of Arts and Science, Department of Mathematics, Bursa Uludag University, 16059 Bursa-Turkey
bFaculty of Arts and Science, Department of Mathematics, Bursa Uludag University, 16059 Bursa-Turkey
cFaculty of Arts and Science, Department of Mathematics, Bursa Uludag University, 16059 Bursa-Turkey
dFaculty of Arts and Science, Department of Mathematics, Bursa Uludag University, 16059 Bursa-Turkey
Received: 16 December 2019, Accepted: 6 May 2020, Available online: 23 September 2020.
Corresponding Author: Ismail Naci Cangul (Email address: cangul@uludag.edu.tr)
Full Text: PDF
Abstract
A recently introduced graph invariant Ω(G) for a graph G is proven to have several nice applications in Graph Theory and Combinatorics. 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.
Keywords: Line graph, Omega invariant, Degree sequence
References:- J. A. Bondy and U. S. R. Murty, Graph Theory, Springer, NY, 2008.
- S. Delen and I. N. Cangul, A New Graph Invariant, Turkish Journal of Analysis and Number Theory 6 (1), 30-33, 2018.
- R. Diestel, Graph Theory, Springer, GTM, 2010.
- L. R. Foulds, Graph Theory Applications, Springer Universitext, 1992.
- H. Ozden, F. Ersoy Zihni, F. Ozen Erdogan, I. N. Cangul, G. Srivastava and H. M. Srivastava, Independence Number of Graphs and Line Graphs of Trees by Means of Omega Invariant, Revista de la Real Academia de Ciencias Exactas Fsicas y Naturales. Serie A. Matemticas 114, 91, 2020.