New Chromatic and Symmetric Extensions of Dominance in Structured Graphs

Abstract

Domination theory is essential for understanding control and influence in network architectures. Traditional domination parameters are primarily concerned with coverage and adjacency, frequently overlooking the implications of colour limitations, internal connectedness and structural symmetry. In order to fill these gaps, this paper presents three new domination extensions: Symmetric Mirror Domination (SMD), Chromatic Restraint Domination (CRD) and Inter-Domination Sets (IDS). These extensions are examined on three structured graph families: Double Star Bridge Graph, Mirror Linked Path Graph and Skip Wheel Graph. These findings pave the way for further research into the structural and combinatorial aspects of graph domination.