TY - JOUR
ID - 109818
TI - Strong rainbow coloring of unicyclic graphs
JO - Khayyam Journal of Mathematics
JA - KJM
LA - en
SN -
AU - Rostami, Amin
AU - Mirzavaziri, Madjid
AU - Rahbarnia, Freydoon
AD - Department of Pure Mathematics, Ferdowsi University
of Mashhad, P.O. Box 1159, Mashhad 91775, Iran
AD - Department of Applied Mathematics, Ferdowsi
University of Mashhad, P.O. Box
1159, Mashhad 91775, Iran.
Y1 - 2020
PY - 2020
VL - 6
IS - 2
SP - 206
EP - 216
KW - Rainbow connection number
KW - strong rainbow connection number
KW - unicyclic graph
DO - 10.22034/kjm.2020.109818
N2 - 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.
UR - http://www.kjm-math.org/article_109818.html
L1 - http://www.kjm-math.org/article_109818_301fa61eefbf5cce342037ce7790283b.pdf
ER -