Affiliation:
1. Department of Mathematics, SASTRA Deemed to be University, Thanjavur 613401, Tamilnadu, India
Abstract
The problem of strong edge coloring discusses assigning colors to the edges of a graph such that distinct colors are assigned to any two edges which are either adjacent to each other or are adjacent to a common edge. The least number of colors required to define a strong edge coloring of a graph is called its strong chromatic index. This problem is equivalent to the problem of assigning collision-free frequencies to the links between the elements of a wireless sensor network. In this article, we discuss a novel way of generating new graphs from existing graphs. This graph construction is known as inflating a graph. We discuss the strong chromatic index of graphs generated by inflating some common classes of graphs and graphs derived from them. In particular, we consider the cycle graph, which is symmetric in nature, and graphs such as the path graph and the star graph, which are not symmetric. Further, we analyze the factors which influence the strong chromatic index of these inflated graphs.
Subject
Physics and Astronomy (miscellaneous),General Mathematics,Chemistry (miscellaneous),Computer Science (miscellaneous)
Reference34 articles.
1. Frequency assignment: Theory and applications;Hale;Proc. IEEE,1980
2. Halász, G., and Sós, V.T. (2012). Irregularities of Partitions, Springer Science and Business Media.
3. On strong edge-coloring of graphs with maximum degree 4;Lv;Discret. Appl. Math.,2018
4. Strong chromatic index of graphs with maximum degree four;Huang;Electron. J. Comb.,2018
5. On the precise value of the strong chromatic index of a planar graph with a large girth;Chang;Discret. Appl. Math.,2018