International Journal of Nonlinear Analysis and Applications

The operations effects on the line graphs of simple graphs

Document Type : Research Paper

Author

Department of Mathematics and Statics, Mutah University, Al-Karak, Jordan

Abstract

The line graph of the graph $\Gamma$ denoted by $L(\Gamma)$ is a graph with a vertex set consists of the sets of edges of $\Gamma$ and two vertices are adjacent in $L(\Gamma)$ if they are incident in $\Gamma$. In this article, we discuss and determine the effect of operations on the line graphs of simple graphs.

Keywords

[1] N. Biggs, Algebraic Graph Theory, Cambridge University Press, 1993.
[2] G. Chartrand, L. Linda and Z. Ping, Graphs and Diagraphs, CRC Press, 2010.
[3] J. Clark and D.A. Holton, A First Look at Graph Theory, World Scientific Co. Pte. Ltd. 1991.
[4] F. Doujan Wrikat, On the complements of graphs, Int. J. Math. Computer Sci. 15(3) (2020) 839–843.
[5] J. Elles and D. Toledo, Hassler Whitney Collected Papers, Birkh¨auser Basel, Springer, 1992.
[6] L. Euler, Solutio prblematis geometrias Situs pertinentis, Comment Acadima Sci. I Petropltance 8 (1766) 128–140.
[7] F. Harary, Graph Theory, Addison-Wesley, Massachusetts, 1994.
[8] A. Hoffman, On the line graph of the complete graph, Ann. Math. Stat. 35(2) (1984) 883–885.
[9] F. Harary, Graph Theory, Wesley, 1994.
International Journal of Nonlinear Analysis and Applications
Volume 13, Issue 1
March 2022
Pages 813-816
  • Receive Date: 03 August 2021
  • Accept Date: 27 September 2021