Rainbow Connection Number of Shackle Graphs

DOI

10.2991/acsr.k.220202.013How to use a DOI?

Keywords

Rainbow coloring; Rainbow connection; Shackle graph

Abstract

Let G be a simple, finite and connected graph. For a natural number k, we define an edge coloring c: E(G) → {1,2,…, k} where two adjacent edges can be colored the same. A u – v path (a path connecting two vertices u and v in V(G)) is called a rainbow path if no two edges of path receive the same color. If there exists a u – v rainbow path for any two distinct vertices in V(G), then G is called rainbow connected. In this case, c is called a rainbow k –coloring. The rainbow connection number of G, denoted by rc(G), is the smallest number k such that G has a rainbow k –coloring. In this paper, we obtain upper and lower bounds of rainbow connection number of shackle graph G for any graph G. Furthermore, we show that these bounds are sharp. Then, we get the exact value of rainbow connection number of shackle sun graph, friendship, cycle, complete graph with one edge removed, and fan graph with two certain spokes removed.

Copyright

© 2022 The Authors. Published by Atlantis Press International B.V.

Open Access

This is an open access article under the CC BY-NC license.

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TY  - CONF
AU  - M. Ali Hasan
AU  - Risma Yulina Wulandari
AU  - A.N.M. Salman
PY  - 2022
DA  - 2022/02/08
TI  - Rainbow Connection Number of Shackle Graphs
BT  - Proceedings of the  International Conference on Mathematics, Geometry, Statistics, and Computation (IC-MaGeStiC 2021)
PB  - Atlantis Press
SP  - 58
EP  - 64
SN  - 2352-538X
UR  - https://doi.org/10.2991/acsr.k.220202.013
DO  - 10.2991/acsr.k.220202.013
ID  - Hasan2022
ER  -