soShearEnergy of permutation of necklace

soShearEnergy of permutation of necklace

**Authors : **

J. Chithra ^{1* }and S.P. Jeyakokila ^{2}

**Author Address : **

^{1,2} Department of Mathematics, Lady Doak College, Madurai-625002, India.

*Corresponding author.

**Abstract : **

$Pnueli$, $Lempel$ and $Even$ introduced Permutation Graphs in 1971 {f {cite{Pnueli2}}}. If $i, j$ belong to a permutation on $p$ symbols ${1, 2,ldots, p}$ and if $i$ is less than $j$ then there is an edge between $i$ and $j$ in the permutation graph if $i$ appears after $j$ in the corresponding sequence. A subset D of A, whose closed neighborhood is A in $pi$ is a dominating set of $pi.$ Energy of a graph with respect to the minimal dominating set was introduced by $B.D.Acharya et al$ {f {cite{56}}}. soShearEnergy is introduced in {f {cite{10}}} . In this paper necklace graph is realized as a permutation graph and soShearEnergy of permutation of necklace is calculated with respect to minimal dominating set.

**Keywords : **

Permutation graphs, Necklace, Domination of first kind and second kind, soShearEnergy.

**DOI : **

**Article Info : **

*Received : * December 21, 2018; *Accepted : * February 11, 2019.