TY - GEN

T1 - (Strong) rainbow connection on the splitting of 3-path

AU - Septyanto, F.

AU - Ariyanti, Kiki

N1 - Publisher Copyright:
© 2017 Author(s).

PY - 2017/7/10

Y1 - 2017/7/10

N2 - The rainbow connection number of a graph G, denoted rc(G), is the smallest number of colors needed to color the edges of G so that any two vertices are connected by a path whose edges all have different colors. Similarly we define the strong rainbow connection number of G, denoted by src(G), by replacing "path" with "geodesic". n this paper, we study the rc and src of a very specific construction known as splitting. For any graph H and any m ∈ N, its m-splitting is a new graph denoted by Splm (G) constructed as follows. Suppose V(H) = {h1, ..., hn}. Then for each hi we introduce m new vertices νi1,...,νim and we join each new vertex νij to all neighbors of the original vertex hi in H. In this paper we determine the rc and src of Splm (P3) for all m ∈ N, where P3 is the 3-path, i.e. path with three vertices.

AB - The rainbow connection number of a graph G, denoted rc(G), is the smallest number of colors needed to color the edges of G so that any two vertices are connected by a path whose edges all have different colors. Similarly we define the strong rainbow connection number of G, denoted by src(G), by replacing "path" with "geodesic". n this paper, we study the rc and src of a very specific construction known as splitting. For any graph H and any m ∈ N, its m-splitting is a new graph denoted by Splm (G) constructed as follows. Suppose V(H) = {h1, ..., hn}. Then for each hi we introduce m new vertices νi1,...,νim and we join each new vertex νij to all neighbors of the original vertex hi in H. In this paper we determine the rc and src of Splm (P3) for all m ∈ N, where P3 is the 3-path, i.e. path with three vertices.

UR - http://www.scopus.com/inward/record.url?scp=85026196653&partnerID=8YFLogxK

U2 - 10.1063/1.4991235

DO - 10.1063/1.4991235

M3 - Conference contribution

AN - SCOPUS:85026196653

T3 - AIP Conference Proceedings

BT - International Symposium on Current Progress in Mathematics and Sciences 2016, ISCPMS 2016

A2 - Sugeng, Kiki Ariyanti

A2 - Triyono, Djoko

A2 - Mart, Terry

PB - American Institute of Physics Inc.

T2 - 2nd International Symposium on Current Progress in Mathematics and Sciences 2016, ISCPMS 2016

Y2 - 1 November 2016 through 2 November 2016

ER -