TY - JOUR

T1 - On d-local strong rainbow connection number of prism graphs

AU - Nugroho, E.

AU - Sugeng, K. A.

N1 - Funding Information:
The authors are supported by Universitas Indonesia Research Grant NO. NKB - 2412/UNZ.RST/HKP.05.00/2020.
Publisher Copyright:
© 2021 Institute of Physics Publishing. All rights reserved.
Copyright:
Copyright 2021 Elsevier B.V., All rights reserved.

PY - 2021/1/7

Y1 - 2021/1/7

N2 - A u − v rainbow path is a path that connects two vertices u and v in a graph G and every edge in that path has a different color. A connected graph G is called a rainbow graph if there is a rainbow path for every pair of vertices in G. For any two vertices u and v in G, a rainbow u − v geodesic in G is the shortest rainbow u − v path. The d-local strong rainbow number (lsrcd) is the smallest number of colors needed to color the edges of G such that any two vertices with distance at most d can be connected by a rainbow geodesic. Thus, the value of d is in the interval 1 < d < diam(G). In this paper, we show the lsrcd of prism graphs with d = 2 and d = 3, and the generalized formula of lsrcd for any value of d.

AB - A u − v rainbow path is a path that connects two vertices u and v in a graph G and every edge in that path has a different color. A connected graph G is called a rainbow graph if there is a rainbow path for every pair of vertices in G. For any two vertices u and v in G, a rainbow u − v geodesic in G is the shortest rainbow u − v path. The d-local strong rainbow number (lsrcd) is the smallest number of colors needed to color the edges of G such that any two vertices with distance at most d can be connected by a rainbow geodesic. Thus, the value of d is in the interval 1 < d < diam(G). In this paper, we show the lsrcd of prism graphs with d = 2 and d = 3, and the generalized formula of lsrcd for any value of d.

UR - http://www.scopus.com/inward/record.url?scp=85100759701&partnerID=8YFLogxK

U2 - 10.1088/1742-6596/1722/1/012053

DO - 10.1088/1742-6596/1722/1/012053

M3 - Conference article

AN - SCOPUS:85100759701

VL - 1722

JO - Journal of Physics: Conference Series

JF - Journal of Physics: Conference Series

SN - 1742-6588

IS - 1

M1 - 012053

T2 - 10th International Conference and Workshop on High Dimensional Data Analysis, ICW-HDDA 2020

Y2 - 12 October 2020 through 15 October 2020

ER -