Advances and Applications in Discrete Mathematics

The Advances and Applications in Discrete Mathematics is a prestigious peer-reviewed journal indexed in the Emerging Sources Citation Index (ESCI). It is dedicated to publishing original research articles in the field of discrete mathematics and combinatorics, including topics such as graphs, coding theory, and block design. The journal emphasizes efficient and powerful tools for real-world applications and welcomes expository articles that highlight current developments in the field.

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2-OUTER-INDEPENDENT SEMITOTAL DOMINATION IN GRAPHS

Authors

  • Sergio R. Canoy
  • Alkajim A. Aradais

Keywords:

outer-independent, semitotal domination, independence number, complementary prism, lexicographic product.

DOI:

https://doi.org/10.17654/0974165822026

Abstract

In this paper, we introduce the concepts of a 2-outer-independent semitotal dominating set and the corresponding parameter 2-outer-independent semitotal domination number of a graph. We determine bounds (or exact values) of the 2-outer-independent semitotal domination number of some graphs. Also, we show that for graphs without isolated vertices, the 2-outer-independent semitotal domination and 2-outer-independent domination are equivalent concepts.

Received: March 14, 2022
Revised: April 26, 2022
Accepted: May 2, 2022

References

I. S. Aniversario, S. R. Canoy, Jr. and F. P. Jamil, On semitotal domination in graphs, Eur. J. Pure Appl. Math. 12(4) (2019), 1410-1425.

Esther Galby, Andrea Munaro and Bernard Ries, Semitotal domination: new hardness results and a polynomial-time algorithm for graphs of bounded mim-width, Theoret. Comput. Sci. 814 (2020), 28-48.

W. Goddard, M. A. Henning and C. A. McPillan, Semitotal domination in graphs, Util. Math. 94 (2014), 67-81.

Z. Wei and H. Guoliang, Semitotal domination in trees, Discrete Math. Theor. Comput. Sci. 20(2) (2018), 1-11.

M. A. Henning and A. J. Marcon, On matching and semitotal domination in graphs, Discrete Math. 324 (2014), 13-18.

M. A. Henning and A. J. Marcon, Semitotal domination in claw-free cubic graphs, Ann. Comb. 20(4) (2016), 799-813.

M. A. Henning and A. Pandey, Algorithmic aspects of semitotal domination in graphs, Theoret. Comput. Sci. 766 (2019), 46-57.

N. J. Rad and M. Krzywkowski, 2-outer-independent domination in graphs, Nat. Acad. Sci. Lett. 38 (2015), 263-269.

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Published

2022-05-19

Issue

Vol. 31 (2022)

Section

Articles

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How to Cite

2-OUTER-INDEPENDENT SEMITOTAL DOMINATION IN GRAPHS. (2022). Advances and Applications in Discrete Mathematics, 31, 67-85. https://doi.org/10.17654/0974165822026

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