%0 Journal Article
%T Strong rainbow coloring of unicyclic graphs
%J Khayyam Journal of Mathematics
%I 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)
%Z 2423-4788
%A Rostami, Amin
%A Mirzavaziri, Madjid
%A Rahbarnia, Freydoon
%D 2020
%\ 07/01/2020
%V 6
%N 2
%P 206-216
%! Strong rainbow coloring of unicyclic graphs
%K Rainbow connection number
%K strong rainbow connection number
%K unicyclic graph
%R 10.22034/kjm.2020.109818
%X 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.
%U http://www.kjm-math.org/article_109818_301fa61eefbf5cce342037ce7790283b.pdf