ON THE LOCATING RAINBOW CONNECTION NUMBER FOR CORONA PRODUCT OF GRAPHS

• Main Author: Dharia M Taihuttu, Pranaya
• Format: Theses
• Language: Indonesia
• Online Access: https://digilib.itb.ac.id/gdl/view/53761
• Institution: Institut Teknologi Bandung

Let k be a positive integer and G = (V;E) be a finite and connected graph. A path P of G whose all internal vertices have distinct colors is called a rainbow vertex path. A vertex k-coloring of G is function c : V (G) ! f1; 2; ; kg such that for every u and v in V (G) there exists a rainbow vertex path that connects them. For i 2 f1; 2; ; kg, let Ri be a set of vertex with color i and = fR1;R2; : : : ;Rkg be an ordered partition of V (G). The rainbow code of a vertex v 2 V (G) with respect to is defined as the k-tuple rc(v) = (d(v;R1); d(v;R2); : : : ; d(v;Rk)) with d(v;Ri) = minfd(v; y)jy 2 Rig for i 2 f1; 2; ; kg. If every vertex of G has distinct rainbow codes, then c is called a locating rainbow k-coloring of G. The locating rainbow connection number of G, denoted by rvcl(G), is defined as the smallest positive integer k such that G has a locating rainbow k-coloring. In this thesis, we give a lower bound and an upper bound for the locating rainbow connection number of corona product of a connected graph G with a graph H. Furthermore, we determine the locating rainbow connection number of corona product of any connected graph G with a graph H, where H is the complement of a complete graph, a complete graph, or a star graph.