Rainbow connection and strong rainbow connection number on the corona product of sandat graphs

Rainbow connection and strong rainbow connection number on the corona product of sandat graphs

Edge coloring in a graph is called a rainbow connected if each pair of graph vertices has a rainbow path (i.e., a path with distinct edge colors). The fewest colors utilized so that each pair of graph vertices has a rainbow path is called a rainbow connection number. Meanwhile, if each pair of graph...

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Hauptverfasser: Saputri, Ainin Yusri, Susanto, Hery, Rahmadani, Desi
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Apexes
Graph coloring
Graph theory
Graphs
Shortest-path problems
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Susanto, Hery
Rahmadani, Desi
description Edge coloring in a graph is called a rainbow connected if each pair of graph vertices has a rainbow path (i.e., a path with distinct edge colors). The fewest colors utilized so that each pair of graph vertices has a rainbow path is called a rainbow connection number. Meanwhile, if each pair of graph vertices has the shortest path with no edges of the same color, this graph can be called strongly rainbow connected. This path is best known as a rainbow geodesic. The strong rainbow connection number is the fewest colors utilized so that every two vertices in a graph have a rainbow geodesic. In this paper, we determine a strong rainbow connection number of sandat graphs as well as a rainbow and strong rainbow connection numbers of graphs that are obtained from the corona product between a sandat graph St(n) and the complement complete graph Kn¯. For the results, we obtained that a strong rainbow connection number of St (n) = n with n > 1, and a rainbow and strong rainbow connection number on the corona product of sandat graphs with n > 1, equals the number of pendant edges.
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subjects Apexes
Graph coloring
Graph theory
Graphs
Shortest-path problems
title Rainbow connection and strong rainbow connection number on the corona product of sandat graphs
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