On the Enclave Domination Number in Some Special Graph Families and Its Applications
M. Santhosh Priya *
PG & Research Department of Mathematics, The Standard Fireworks Rajaratnam College for Women (Autonomous), Sivakasi-626123, Affiliated to Madurai Kamaraj University, Madurai, Tamil Nadu, India.
A. Mydeen Bibi
PG & Research Department of Mathematics, The Standard Fireworks Rajaratnam College for Women (Autonomous), Sivakasi-626123, Affiliated to Madurai Kamaraj University, Madurai, Tamil Nadu, India.
*Author to whom correspondence should be addressed.
Abstract
Domination is a classical concept in graph theory that has given rise to numerous refinements and generalizations. This paper investigates a domination variant referred to as the enclave dominating set. The exact values of the enclave domination number are determined for several families of special graphs, such as Jellyfish, Jewel, Dutch windmill, lollipop, comb, sunlet, crown, and friendship graphs, as well as for the Soifer, Franklin, Moser spindle, Chv´atal, Fritsch, Herschel, and Goldner–Harary graphs. All enclave dominating vertices and their corresponding minimum enclave dominating sets are characterized. These results advance the theoretical framework of the enclave domination parameter, provide new insights into graph structures, and highlight applications of enclave dominating sets.
Keywords: Domination number, enclave dominating vertex, enclave dominating set, enclave domination number