Induced Dominating Sequence and ESD Graphs

Induced Dominating Sequence and ESD Graphs


  • Indulal Gopalapilla St Aloysius College, Edathua
  • Liju Alex
  • John Joy



dominating set, domination number, induced domination sequence, Equally significant dominating(ESD) graph, induced domination index


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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How to Cite

I. Gopalapilla, L. Alex, and J. J. . Mulloor, “Induced Dominating Sequence and ESD Graphs: Induced Dominating Sequence and ESD Graphs”, Proyecciones (Antofagasta, On line), vol. 43, no. 4, pp. 947-964, Jun. 2024.




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