Induced Dominating Sequence and ESD Graphs
DOI:
https://doi.org/10.22199/issn.0717-6279-6179Keywords:
dominating set, domination number, induced domination sequence, Equally significant dominating(ESD) graph, induced domination indexAbstract
A vertex subset D of a graph G = (V,E) is said to be a dominating set if every vertex in G is either in D or adjacent to some vertex in D. The minimum cardinality of such a set is the domination number, which is denoted as γ(G). In this paper, we define a sequence associated with the domination concept in graphs and studied the basic properties of the sequence in terms of various parameters of graphs. Using this sequence we order the vertices of a dominating set according its significance and propose Equally Significant Dominating (ESD) graphs. We also introduced domination related topological indices and compute their lower bounds for trees, unicyclic graphs and bicyclic graphs. All the graphs attaining the bounds are characterized.
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Copyright (c) 2024 Indulal Gopalapilla, Liju Alex, John Joy
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