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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SECURE DOMINATING SETS AND SECURE DOMINATION POLYNOMIALS OF CYCLES

Authors

  • K. Lal Gipson
  • T. Subha

Keywords:

domination, secure dominating set, secure dominating number, secure domination polynomial.

DOI:

https://doi.org/10.17654/0974165822006

Abstract

In this paper, we study the secure dominating sets of cycles and  secure domination polynomials of cycles in graph theory. We obtain the recursive formulas for the coefficients of secure domination polynomials of cycles. Using these recursive formulas, we construct the polynomial, which we call secure domination polynomial of the cycle and also obtain some properties of this polynomial.

Received: July 13, 2021
Revised: September 21, 2021
Accepted: November 20, 2021

References

S. Alikhani and Y.-H. Peng, Dominating sets and domination polynomials of certain graphs, II, Opuscula Math. 30(1) (2010), 37-51.

G. Chartrand and L. Lesniak, Graphs and Digraphs, 4th ed., Chapman & Hall/CRC, 2005.

E. J. Cockayne, P. J. P. Grobler, W. R. Grundlingh, J. Munganga and J. H. Van Vuuren, Protection of a graph, Util. Math. 67 (2005), 19-32.

S. V. Divya Rashmi, S. Arumugam and Ibrahim Venkat, Secure domination in graphs, Int. J. Adv. Soft Comput. Appl. 8(2) (2016), 79-83.

T. W. Haynes, S. T. Hedetniemi and P. J. Slater, Fundamentals of Domination in Graphs, Marcel Dekker, New York, 1998.

K. Lal Gipson and T. Subha, Secure domination polynomials of paths, International J. Scientific and Technology Research 9(2) (2020), 6517-6521.

A. Vijayan and K. Lal Gipson, Dominating sets and domination polynomials of square of cycles, IOSR Journal of Mathematics (IOSR-JM) 3(4) (2012), 4-14.

Published

2021-12-20

Issue

Section

Articles

How to Cite

SECURE DOMINATING SETS AND SECURE DOMINATION POLYNOMIALS OF CYCLES. (2021). Advances and Applications in Discrete Mathematics, 29(1), 59-83. https://doi.org/10.17654/0974165822006

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