Rainbow connection number of generalized composition
نویسندگان
چکیده
منابع مشابه
Rainbow Connection Number and Connectivity
The rainbow connection number, rc(G), of a connected graph G is the minimum number of colors needed to color its edges, so that every pair of vertices is connected by at least one path in which no two edges are colored the same. Our main result is that rc(G) ≤ dn2 e for any 2-connected graph with at least three vertices. We conjecture that rc(G) ≤ n/κ + C for a κ-connected graph G of order n, w...
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The rainbow connection number, rc(G), of a connected graph G is the minimum number of colours needed to colour its edges, so that every pair of its vertices is connected by at least one path in which no two edges are coloured the same. In this note we show that for every bridgeless graph G with radius r, rc(G) ≤ r(r + 2). We demonstrate that this bound is the best possible for rc(G) as a functi...
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A path in an edge colored graph is said to be a rainbow path if every edge in this path is colored with the same color. The rainbow connection number of G, denoted by rc(G), is the smallest number of colors needed to color its edges, so that every pair of its vertices is connected by at least one rainbow path. A rainbow u − v geodesic in G is a rainbow path of length d(u, v), where d(u, v) is t...
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An edge-colored graph G is rainbow connected, if any two vertices are connected by a path whose edges have distinct colors. The rainbow connection number of a connected graph G, denoted rc(G), is the smallest number of colors that are needed in order to make G rainbow connected. In this paper we show that rc(G) ≤ 3 if |E(G)| ≥ ( n−2 2 ) + 2, and rc(G) ≤ 4 if |E(G)| ≥ ( n−3 2 ) + 3. These bounds...
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Rainbow connection number, rc(G), of a connected graph G is the minimum number of colours needed to colour its edges, so that every pair of vertices is connected by at least one path in which no two edges are coloured the same. In this paper we investigate the relationship of rainbow connection number with vertex and edge connectivity. It is already known that for a connected graph with minimum...
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ژورنال
عنوان ژورنال: AKCE International Journal of Graphs and Combinatorics
سال: 2020
ISSN: 0972-8600,2543-3474
DOI: 10.1016/j.akcej.2018.10.001