THE 4-RAINBOW INDEX OF CM + PN

• Main Author: Yefri Fadhilah, Suci
• Format: Theses
• Language: Indonesia
• Online Access: https://digilib.itb.ac.id/gdl/view/61244
• Institution: Institut Teknologi Bandung

Let G be a simple and connected graph of order n with an h-edge coloring c : E(G) ! f1; 2; : : : ; hg for some h 2 N, where adjacent edges may be colored the same. A tree T in G is called a rainbow tree, if no two edges of T have the same color. An h-edge coloring of G is called a k-rainbow h-edge coloring for some k 2 f2; 3; : : : ; ng, if for every S V (G) with j S j= k, there exists a rainbow tree in G containing the vertices of S. Such a rainbow tree is called a rainbow S????tree. The k-rainbow index of G, denoted by rxk, is the minimum positive integer h such that there is a k-rainbow h-edge coloring of G. Let G1 = (V1;E1) and G2 = (V2;E2) be two graphs. The join of G1 and G2, denoted by G1 + G2, is a graph with the vertex set V (G1 + G2) = V (G1) [ V (G2) and the edge set E(G1 + G2) = E(G1) [ E(G2) [ fuv j u 2 V G1; v 2 V (G2)g. In this thesis, we consider the 4-rainbow index of Cm+Pn for anym 3 and n 1.