@article {
author = {Rostami, Amin and Mirzavaziri, Madjid and Rahbarnia, Freydoon},
title = {Strong rainbow coloring of unicyclic graphs},
journal = {Khayyam Journal of Mathematics},
volume = {6},
number = {2},
pages = {206-216},
year = {2020},
publisher = {Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with the Center of Excellence in Analysis on Algebraic Structures and Tusi Mathematical Research Group)},
issn = {2423-4788},
eissn = {2423-4788},
doi = {10.22034/kjm.2020.109818},
abstract = {A path in an edge-colored graph is called a \textit{rainbow path}, if no two edges of the path are colored the same. An edge-colored graph $G$, is \textit{rainbow-connected} if any two vertices are connected by a rainbow path. A rainbow-connected graph is called strongly rainbow connected if for every two distinct vertices $u$ and $v$ of $V(G)$, there exists a rainbow path $P$ from $u$ to $v$ that in the length of $P$ is equal to $d(u,v)$. The notations {\rm rc}$(G)$ and {\rm src}$(G)$ are the smallest number of colors that are needed in order to make $G$ rainbow connected and strongly rainbow connected, respectively. In this paper, we find the exact value of {\rm rc}$(G)$, where $G$ is a unicyclic graph. Moreover, we determine the upper and lower bounds for {\rm src}$(G)$, where $G$ is a unicyclic graph, and we show that these bounds are sharp.},
keywords = {Rainbow connection number,strong rainbow connection number,unicyclic graph},
url = {http://www.kjm-math.org/article_109818.html},
eprint = {http://www.kjm-math.org/article_109818_301fa61eefbf5cce342037ce7790283b.pdf}
}