Star Chromatic Index of Some Types of Graphs
C.L.R. Fernando *
Department of Mathematics, Faculty of Science, University of Peradeniya, Sri Lanka.
A.M.C.U.M. Athapattu
Department of Mathematics, Faculty of Science, University of Peradeniya, Sri Lanka.
*Author to whom correspondence should be addressed.
Abstract
This research explores the concept of star edge coloring, more specifically, it studies the star edge coloring of pan graphs (Tn,1), tadpole graphs (Tn,m), friendship graphs (Fn), ladder graphs (Ln), flower graphs (U2,m), and umbrella graphs (Un,m). Based on previous work, utilizing the established upper bounds and known results from the star edge coloring of paths, cycles, and stars, X'st(G) has been proven for those graph types. Beyond theoretical analysis, this study provides a method for constructing a valid star edge coloring for those families of graphs. The proposed algorithms are generic and can be applied to numerous classes of graphs with similar features.
Keywords: Friendship graph, ladder graph, star chromatic index, star edge coloring, star graph, tadpole graph, umbrella graph