Edge covering coloring of cartesian product and compositions of graphs

• Main Author: Santos, Bernadette Louise Y.
• Format: text
• Language: English
• Published: Animo Repository 2016
• Subjects: Charts; diagrams; etc; Graphic methods; Complete graphs; Graph theory
• Online Access: https://animorepository.dlsu.edu.ph/etd_masteral/5460
• Institution: De La Salle University

An edge coloring of a graph G is called an edge covering coloring if each color appears at each vertex at least once. The maximum positive integer k such that G has an edge covering coloring with k colors is called the edge covering chromatic index of G and is denoted by 0 c(G). A result from Gupta [4] enables us to conclude that for any graph G with minimum degree (G), we have (G){u100000}1 0 c(G) (G). This allows us to classify graphs as CI class if 0 c(G) = (G) and CII class otherwise. In the literature, the classification of different types of graphs such as bipartite graphs, peelable graphs, and double graphs, among others, has already been done. However, there were no studies found on the classification of the cartesian product and the composition of graphs. This paper aims to study the classification of these graphs as either CI or CII class graphs.