Independent Domination Degree of Standard Graphs of Adriatic \((a,b)\)-KA Indices

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DOI:

https://doi.org/10.26713/cma.v14i4.2579

Keywords:

Topological index, Adriatic (a,b)-KA index, Independent degree domination, Independent minimal dominating number

Abstract

The dominating set \(D\) of the graph \(K=(V,E)\) is the independent dominating set (Ids), the independent domination number \(i(K)\) of the graph \(K\) is the minimum cardinality of id. In this article, we introduce the new independent degree domination (idd) of each vertices \(s\in V(K)\), denoted by \(d_{id}(s)\) and compute the Adriatic \((a,b)\)-KA index for book graphs, cycle middle graphs and windmill graphs.

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References

M. O. Albertson, The irregularity of a graph, Ars Combinatoria 46 (1997), 219 – 225.

A. Alwardi, A. Alqesmah, R. Rangarajan and I. N. Cangul, Entire Zagreb indices of graphs, Discrete Mathematics, Algorithms and Applications 10(3) (2018), 1850037, DOI: 10.1142/S1793830918500374.

M. Atapour, A. Jahanbani and R. Khoeilar, New bounds for the Randic index of graphs, Journal of Mathematics 2021 (2021), Article ID 9938406, 8 pages, DOI: 10.1155/2021/9938406.

F. V. Fomin, F. Grandoni, A. V. Pyatkin and A. A. Stepanov, On maximum number of minimal dominating sets in graphs, Electronic Notes in Discrete Mathematics 22 (2005), 157 – 162, DOI: 10.1016/j.endm.2005.06.028.

W. Goddard and M. A. Henning, Independent domination in graphs: A survey and recent results, Discrete Mathematics 313(7) (2013), 839 – 854, DOI: 10.1016/j.disc.2012.11.031.

I. Gutman, M. Togan, A. Yurttas, A. S. Cevik and I. N. Cangul, Inverse problem of sigma index, MATCH Communications in Mathematical and in Computer Chemistry 79 (2018), 491 – 508, URL: https://match.pmf.kg.ac.rs/electronic_versions/Match79/n2/match79n2_491-508.pdf.

T. W. Haynes, S. Hedetniemi and P. Slater, Fundamentals of Domination in Graphs, 1st edition, CRC Press, Boca Raton, 464 pages (1998), DOI: 10.1201/9781482246582.

A. Jahanbani and H. Shooshtary, Nano-Zagreb index and multiplicative nano-zagreb index of some graph operations, International Journal of Computing Science and Applied Mathematics 5(1) (2019), 15 – 22, DOI: 10.12962/j24775401.v5i1.4659.

V. R. Kulli, Minus F and square F-indices and their polynomials of certain dendrimers, Earthline Journal of Mathematical Sciences 1(2) (2019), 172 – 185, DOI: 10.34198/ejms.1219.171185.

V. R. Kulli, B. Chaluvaraju and T. Vidya, Computation of adriatic (a,b)-KA index of some nanostructues, International Journal of Mathematics Trends and Technology 67(4) (2021), 79 – 87, DOI: 10.14445/22315373/IJMTT-V67I4P511.

V. Lokesha, K. Z. Yasmeen, B. Chaluvaraju and T. Deepika, Computation of misbalance type degree indices of certain classes of derived graph, International Journal of Mathematical Combinatorics 3 (2019), 61 – 69, URL: https://fs.unm.edu/IJMC/IJMC-3-2019.pdf.

T. Réti, R. Sharfdini, Á. D. Kiss and H. Hagobin, Graph irregularity indices used as molecular Descriptors in QSPR studies, MATCH Communications in Mathematical and in Computer Chemistry 79 (2018), 509 – 524, URL: https://match.pmf.kg.ac.rs/electronic_versions/Match79/n2/match79n2_509-524.pdf.

M. L. Roden and P. J. Slater, Liar’s domination in graphs, Discrete Mathematics 309(19) (2009), 5884 – 5890, DOI: 10.1016/j.disc.2008.07.019.

D. Vukicevic and M. Gasperov, Bond additive modeling 1. Adriatic indices, Croatica Chemica Acta 83(3) (2010), 243 – 260, URL: https://hrcak.srce.hr/file/93215.

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Published

25-12-2023
CITATION

How to Cite

Mekala, A., Kumar, U. V. C., & Murali, R. (2023). Independent Domination Degree of Standard Graphs of Adriatic \((a,b)\)-KA Indices. Communications in Mathematics and Applications, 14(4), 1421–1428. https://doi.org/10.26713/cma.v14i4.2579

Issue

Vol. 14 No. 4 (2023)

Section

Research Article

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