Detour domination number of some path and cycle related graphs
Authors :
S. K. Vaidya 1 * and S. H. Karkar 2
Author Address :
1 Department of Mathematics, Saurashtra University, Rajkot-360005, Gujarat, India.
2 Department of Mathematics, Government Engineering College, Rajkot-360005, Gujarat, India.
*Corresponding author.
Abstract :
The detour distance $D(u, v)$ between two vertices of a connected graph $G$ is the length of a longest path between them. A set $S$ of vertices of $G$ is called a extit{detour dominating set} if every vertex of $G$ is detour dominated by some vertex in $S$. A detour dominating set of minimum cardinality is a extit{minimum detour dominating set} and its cardinality is the extit{ detour domination number} $gamma_{_{D}}(G)$. We have investigated detour domination number of larger graphs obtained from path and cycles by means of various graph operations.
Keywords :
Domination number, Detour distance, Detour domination number.
DOI :
Article Info :
Received : August 10, 2018; Accepted : December 12, 2018.
