The Minimum Superior Dominating Energy of Graphs
Tejaskumar R *
PG & Research Department of Mathematics, Jamal Mohamed College (Affiliated to Bharathidasan University), Tiruchirappalli-620020, Tamil Nadu, India.
A Mohamed Ismayil
PG & Research Department of Mathematics, Jamal Mohamed College (Affiliated to Bharathidasan University), Tiruchirappalli-620020, Tamil Nadu, India.
*Author to whom correspondence should be addressed.
Abstract
Kathiresan and Marimuthu were the pioneers of superior distance in graphs. The same authors put forth the concept of superior domination in 2008. Superior distance is the shortest walk between any two vertices including their respective neighbours. The minimum superior dominating energy is defined by the sum of the eigenvalues and it is obtained from the minimum superior dominating matrix . The minimum superior dominating energy for star and crown graphs are computed. Properties of eigenvalues of minimum superior dominating matrix for star, cocktail party, complete and crown graphs are discussed. Results related to upper and lower bounds of minimum superior dominating energy for star, cocktail party, complete and crown graphs are stated and proved.
Keywords: Minimum superior dominating set, minimum superior dominating energy, superior distance, superior neighbour, superior dominating eigenvalues