Rainbow Connection Number of the Thorn Graph
نویسندگان
چکیده
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 the distance between u and v. The graph G is strongly rainbow connected if there exists a rainbow u − v geodesic for any two vertices u and v in G. The strong rainbow connection number src(G) of G is the minimum number of colors needed to make G strongly rainbow connected. In this paper, we determine the exact values of rc(G) and src(G) where G are the thorn graph of complete graph K∗ n, the thorn graph of the cycle C∗ n. Mathematics Subject Classification: 05C15, 05C40
منابع مشابه
Some Results on the Maximal 2-Rainbow Domination Number in Graphs
A 2-rainbow dominating function ( ) of a graph is a function from the vertex set to the set of all subsets of the set such that for any vertex with the condition is fulfilled, where is the open neighborhood of . A maximal 2-rainbow dominating function on a graph is a 2-rainbow dominating function such that the set is not a dominating set of . The weight of a maximal is the value . ...
متن کاملRainbow connection in oriented graphs
An edge-coloured graph G is said to be rainbow-connected if any two vertices are connected by a path whose edges have different colours. The rainbow connection number of a graph is the minimum number of colours needed to make the graph rainbow-connected. This graph parameter was introduced by G. Chartrand, G.L. Johns, K.A. McKeon and P. Zhang in 2008. Since, the topic drew much attention, and v...
متن کاملOn the rainbow connection of Cartesian products and their subgraphs
Rainbow connection number of Cartesian products and their subgraphs are considered. Previously known bounds are compared and non-existence of such bounds for subgraphs of products are discussed. It is shown that the rainbow connection number of an isometric subgraph of a hypercube is bounded above by the rainbow connection number of the hypercube. Isometric subgraphs of hypercubes with the rain...
متن کاملOn Rainbow Connection Number and Connectivity
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...
متن کاملComputing Minimum Rainbow and Strong Rainbow Colorings of Block Graphs
A path in an edge-colored graph G is rainbow if no two edges of it are colored the same. The graph G is rainbow-connected if there is a rainbow path between every pair of vertices. If there is a rainbow shortest path between every pair of vertices, the graph G is strongly rainbow-connected. The minimum number of colors needed to make G rainbow-connected is known as the rainbow connection number...
متن کامل