Star Chromatic Index of Subcubic Graphs Kavita Pradeep 1 Department of Mathematics Anna University MIT Campus Chennai, India V Vijayalakshmi 2 Department of Mathematics Anna University MIT Campus Chennai, India Abstract The star chromatic index of a graph G is the minimum number of colors needed to properly color the edges of G so that no path or cycle of length four is bi-colored. In this paper, we show that every subcubic graph with maximum average degree less than 11 5 can be star edge colored with at most five colors. Keywords: Subcubic graph, Maximum average degree, Girth. 1 Introduction A proper edge coloring of a graph G is an assignment f of colors to the edges of G such that f (e) = f (e ′ ) whenever the edges e and e ′ are adjacent in G. 1 Email: kavita2428@gmail.com 2 Email: vijayalakshmi@annauniv.edu Available online at www.sciencedirect.com Electronic Notes in Discrete Mathematics 53 (2016) 155–164 1571-0653/© 2016 Elsevier B.V. All rights reserved. www.elsevier.com/locate/endm http://dx.doi.org/10.1016/j.endm.2016.05.014