Rainbow colouring of certain product graphs

Abstract

Graphs play an essential role in computer science and network analysis, representing complex
relationships among entities. A rainbow colouring of a connected graph is an edge colouring process in which
every pair of vertices is linked by at least one path with distinct coloured edges. This study examines the
rainbow colouring properties of the cyclic product graph G = C(2n, 1), determining its rainbow connection
number rc(G) and strong rainbow connection number src(G). Additional analyses are carried out for corona
product graphs to establish their vertex and strong rainbow connection numbers.