Detour domination number of some path and cycle related graphs

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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 :

10.26637/MJM0701/0004

Article Info :

Received : August 10, 2018; Accepted : December 12, 2018.

 

 

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