Algorithms to determine an independent dominating set of $ESC (n, k)$

S. Pious Missiera,*, A. Anto Kinsleyb and Evangeline Prathibha Fernandoc

Algorithms to determine an independent dominating set of $ESC (n, k)$

Authors :

S. Pious Missier^a,*, A. Anto Kinsley^b and Evangeline Prathibha Fernando^c

Author Address :

^a,*cAssociate Professor, PG and Research Department of Mathematics, V. O. Chidambaram College, Thoothukudi-628008, Tamil Nadu, India.
^bAssociate Professor, PG and Research Department of Mathematics, St. Xavier’s College, Palayamkottai-627001, Tamil Nadu, India.

*Corresponding author.

Abstract :

The independent dominating set is an interesting property used in the allocation of finite resources in a massively parallel network such as the extended star graph with cross-connections ($ESC$). In this paper, we have initially designed algorithms to compute the independent dominating set of $ESC (n, k)$ for $ n = 2$ and $n = 3$. Using the hierarchical nature of the $ESC$ with its basic building block $ESC (n, 1)$ we have designed a generalized algorithm to compute the independent dominating set of $ESC (n, k$) for all $n$ and $k$.