Connected Outer-Hop Independent Dominating Sets in Graphs Under Some Binary Operations

Authors

  • Jahiri Manditong MSU Tawi-Tawi College of Technology and Oceanography
  • Javier Hassan MSU Tawi-Tawi College of Technology and Oceanography
  • Ladznar S. Laja
  • Amy A. Laja
  • Nurijam Hanna M. Mohammad
  • Sisteta U. Kamdon

DOI:

https://doi.org/10.29020/nybg.ejpam.v16i3.4766

Keywords:

connected outer-hop independent dominating set, connected outer-hop independent domination number, domination, connected domination

Abstract

Let $G$ be a connected graph. A set $D\subseteq V(G)$ is called a connected outer-hop independent dominating if
$D$ is a connected dominating set and $V(G)\ D$ is a hop independent set in $G$, respectively. The minimum
cardinality of a connected outer-hop independent dominating set in $G$, denoted by $\gamma_{c}^{ohi}(G)$, is
called the connected outer-hop independent domination number of $G$. In this paper, we introduce and investigated
the concept of connected outer-hop independent domination in a graph. We show that the connected outer-hop
independent domination number and connected outer-independent domination number of a graph are incomparable.
In fact, we find that their absolute difference can be made arbitrarily large. In addition, we characterize
connected outer-hop independent dominating sets in graphs under some binary operations. Furthermore, these
results are used to give exact values or bounds of the parameter for these graphs.

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Published

2023-07-30

Issue

Vol. 16 No. 3: (July 2023)

Section

Nonlinear Analysis

License

Copyright (c) 2023 European Journal of Pure and Applied Mathematics

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How to Cite

Connected Outer-Hop Independent Dominating Sets in Graphs Under Some Binary Operations. (2023). European Journal of Pure and Applied Mathematics, 16(3), 1817-1829. https://doi.org/10.29020/nybg.ejpam.v16i3.4766