On total rainbow k-connected graphs

Yuefang Sun, Zemin Jin and Fengwei Li

Applied Mathematics and Computation, 2017, vol. 311, issue C, 223-227

Abstract: A total-colored graph G is total rainbow connected if any two vertices are connected by a path whose edges and inner vertices have distinct colors. A graph G is total rainbow k-connected if there is a total-coloring of G with k colors such that G is total rainbow connected. The total rainbow connection number, denoted by trc(G), of a graph G is the smallest k to make G total rainbow k-connected. For n, k ≥ 1, define h(n, k) to be the minimum size of a total rainbow k-connected graph G of order n. In this paper, we prove a sharp upper bound for trc(G) in terms of the number of vertex-disjoint cycles of G. We also compute exact values and upper bounds for h(n, k).

Keywords: Total rainbow coloring; Total rainbow connection number; Minimally total rainbow k-connected graph (search for similar items in EconPapers)
Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:311:y:2017:i:c:p:223-227

DOI: 10.1016/j.amc.2017.05.020

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