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(1,2)-Rainbow Connection Number and Connected Dominating Sets
Journal of Interconnection NetworksIn this paper, we first show that for every connected graph [Formula: see text], the [Formula: see text]-rainbow connection number [Formula: see text] is upper bounded by [Formula: see text], where [Formula: see text] is a connected two-way dominating ...
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The rainbow connection number of 2-connected graphs
The rainbow connection number of a graph G is the least number of colours in a (not necessarily proper) edge-colouring of G such that every two vertices are joined by a path which contains no colour twice. Improving a result of Caro et al., we prove that the rainbow connection number of every 2-connected graph with n vertices is at most the ceiling of ...
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Rainbow Vertex Connection Numbers and Total Rainbow Connection Numbers of Middle and Total Graphs
Ars Combinatoria, 2023A vertex-colouring of a graph Γ is rainbow vertex connected if every pair of vertices ( u , v ) in Γ there is a u − v path whose internal vertices have different colours. The rainbow vertex connection number of a graph Γ , is the minimum number of colours needed to make Γ rainbow vertex connected, denoted by r v c ( Γ ) .
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Rainbow 2-Connection Numbers of Cayley Graphs
Information Processing Letters, 2015zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Rainbow connection numbers of Cayley graphs
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List rainbow connection number of graphs
Discrete Applied MathematicsAn edge-coloured path is rainbow if all of its edges have distinct colours. Let $G$ be a connected graph. The rainbow connection number of $G$, denoted by $rc(G)$, is the minimum number of colours in an edge-colouring of $G$ such that, any two vertices ...
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