Further results on nonsplit dom strong domination number

G. Mahadevana,* K.Renukab and C. Sivagnanamc

Further results on nonsplit dom strong domination number

Authors :

G. Mahadevan^a,* K.Renuka^b and C. Sivagnanam^c

Author Address :

^a,bDepartment of Mathematics, Gandhigram Rural Institute - Deemed University & Gandhigram, Dindigul-624302, India.
^cDepartment of General Requirements, College of Applied Sciences, Ibri, Sultanate of Oman.

*Corresponding author.

Abstract :

A subset $S$ of $V$ is called a dom strong dominating set if for every vertex $v\in V-S$, there exists $u_1$, $u_2\in S$ such that $u_1v$, $u_2v\in E(G)$ and $d(u_1)\geq d(v)$. The minimum cardinality of a dom strong dominating set is called the dom strong domination number and is denoted by $\gamma_{ds}(G)$. A dom strong dominating set $S$ is said to be a non split dom strong dominating set if the induced subgraph $\langle V-S\rangle$ is connected. The minimum cardinality of a non split dom strong dominating set is called the non split dom strong domination number of a graph and is denoted by $\gamma_{nsds}(G)$. The connectivity $\kappa(G)$ of a graph $G$ is the minimum number of vertices whose removal results in a disconnected or trivial graph. In this paper, we find an upper bound for the sum of nonsplit dom strong domination number and connectivity of a graph and characterise the corresponding extremal graphs.