Induced Dominating Sequence and ESD Graphs

Induced Dominating Sequence and ESD Graphs

Authors

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

DOI:

https://doi.org/10.22199/issn.0717-6279-6179

Keywords:

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

Abstract

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.

References

R. Balakrishnan and K. Ranganathan, A textbook of graph theory. Springer

Science & Business Media, 2012.

E. J. Cockayne and S. T. Hedetniemi, “Towards a theory of domination in

graphs,” Networks, vol. 7, no. 3, pp. 247–261, 1977.

T. W. Haynes, S. T. Hedetniemi, and M. A. Henning, “Fundamentals of domination,”

in Domination in Graphs: Core Concepts, pp. 27–47, Springer, 2023.

H. L. Royden and P. Fitzpatrick, Real analysis, vol. 2. Macmillan New York,

X. Zhang and H. Zhang, “Some graphs determined by their spectra,” Linear

algebra and its applications, vol. 431, no. 9, pp. 1443–1454, 2009.

V. Samodivkin, “Excellent graphs with respect to domination: subgraphs induced

by minimum dominating sets,” arXiv preprint arXiv:2010.03219, 2020.

T. W. Haynes, S. T. Hedetniemi, and M. A. Henning, Topics in domination

in graphs, vol. 64. Springer, 2020.

D. B. West et al., Introduction to graph theory, vol. 2. Prentice hall Upper

Saddle River, 2001.

Published

2024-06-19

How to Cite

[1]
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.

Issue

Section

Artículos

Most read articles by the same author(s)