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 -