TWIN EDGE COLORING OF SOME PATH AND CYCLE RELATED GRAPHS

Full Article - PDF

Published: 2021-05-19

Page: 38-57


J. NAVEEN *

Department of Mathematics, Government Arts College C. Mutlur, Chidambaram, India.

S. MEENA

Department of Mathematics, Government Arts College C. Mutlur, Chidambaram, India.

*Author to whom correspondence should be addressed.


Abstract

A twin edge -coloring of a graph  is a proper edge -coloring of  with the elements of  so that the induced vertex -coloring, in which the color of a vertex  in  is the sum in  of the colors of the edges incident with  is a proper vertex - coloring. The minimum  for which  has a twin edge k- coloring is called the twin chromatic index of . Twin chromatic index of the splitting graph of path and cycle, middle graph of path and cycle and shadow graph of path and cycle are determined. Twin chromatic index of  is also determined, where  denotes the direct product of  and  are, respectively, the cycle and the path on r vertices each.

Keywords: Twin edge coloring, twin chromatic index, path, cycle, splitting graph, middle graph, shadow graph, direct product


How to Cite

NAVEEN, J., & MEENA, S. (2021). TWIN EDGE COLORING OF SOME PATH AND CYCLE RELATED GRAPHS. Asian Journal of Mathematics and Computer Research, 28(1), 38–57. Retrieved from https://ikprress.org/index.php/AJOMCOR/article/view/6371

Downloads

Download data is not yet available.

References

Bondy JA, Murthy USR. Graph Theory and its Application, (North - Holland), Newyork; 1976.

Andrews E, Helenius L, Johnston D, Verwys J, Zhang P. On Twin edge coloring of graphs, Discuss. Math. Graph Theory. 2014;34:613- 627.

Andrews E, Johnston D, Zhang P. A Twin edge coloring Conjecture, Bulletin of the ICA. 2014;70:28 – 44.

Huan Yang, Shuang Liang Tian, Lang Wang Qing Suo. On twin edge colorings of the direct product of paths, IOP Conf. Series: Journal of Physics: Conf. Series. 2018;1087.

Rajarajachozhan R, Sampathkumar R. Twin edge colorings of certain square graphs and product graphs, Electronic Journal of Graph Theory and Applications. 2016; 4:79-93.