Graph-theoretic foundations of enclave domination numbers in graphs and their combinatorial operations

Let G=(V, E) be a simple graph. A set D⊂V(G) is called a dominating set if every vertex in  is adjacent to at least one vertex in V\D. This study introduces the concepts of enclave dominating vertices and enclave dominating sets in graphs and defines a new domination parameter termed the enclave domination number. The investigation determines the exact number of minimum enclave dominating sets for several standard graphs, as well as for graphs constructed through combinatorial operations involving path and wheel-related structures. In addition, new characterizations are presented, and several fundamental properties of the enclave domination number are established, thereby contributing to the broader understanding of domination theory in graph structures. The enclave dominating vertex and the enclave dominating sets are formally introduced, and new characterizations and key properties of the enclave domination number are provided, highlighting its significance and potential applications within graph theory and related fields.

کلیدواژه ها:

Enclave Dominating Vertex ، Enclave Dominating Set ، Enclave Domination Number