On the Rainbow and Strong Rainbow Connection Numbers of the m-Splitting of the Complete Graph Kn | Zendy

Fendy Septyanto | Zendy; Kiki Ariyanti Sugeng | Zendy

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On the Rainbow and Strong Rainbow Connection Numbers of the m-Splitting of the Complete Graph Kn

Author(s) -

Fendy Septyanto,

Kiki Ariyanti Sugeng

Publication year - 2015

Publication title -

procedia computer science

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.334

H-Index - 76

ISSN - 1877-0509

DOI - 10.1016/j.procs.2015.12.092

Subject(s) - rainbow , combinatorics , edge coloring , graph , connection (principal bundle) , fractional coloring , complete coloring , computer science , path (computing) , mathematics , discrete mathematics , graph power , line graph , physics , optics , geometry , computer network

An edge-coloring of a graph is called rainbow if any two vertices are connected by a path consisting of edges of different colors. The least number of colors in such a coloring is called the rainbow connection number of G, denoted by rc(G). An edge-coloring of a graph is called strong rainbow if any two vertices are connected by a geodesic consisting of edges of different colors. The least number of colors in such a coloring is called the strong rainbow connection number of G, denoted by src(G). In this paper we study the rc and src of the m-splitting of a graph. In particular we study Splm(Kn). We present the exact values of its rc and src in several cases, and we prove several bounds in the other cases

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