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Harary Index for an Algebraic Graph

Year 2023, Volume: 5 Issue: 1, 9 - 13, 30.06.2023

Abstract

Topological indices are used in mathematical chemistry. Distance-based topological indices have a great interest in molecular graph theory. Harary index is one of the distance-based graph invariant. Recently, a dot product graph for an algebraic structure has been studied. In this study, the Harary index of this graph will be given.

References

  • I. Beck, Coloring of Commutating Ring, Journal of Algebra, 116 (1988), 208-226.
  • D. F. Anderson, P. S. Livingston, The Zero-Divisor Graph of a Commutative Ring, Journal of Algebra, 217 (1999), 434-447.
  • F. R. De Meyer, L. De Meyer, Zero-Divisor Graphs of Semigroups, Journal of Algebra, 283 (2005), 190- 198.
  • A. Badawi, On the Dot Product Graph of a Commutative Ring, Communications in Algebra, 43 (2015), 43-50.
  • K. C. Das, N. Akgüneş, A. S. Çevik, On a Graph of Monogenic Semigroups, Journal of Inequalities and Applications, 2013:44 (2013).
  • N. Akgüneş, B. Çağan, On the Dot Product of Graphs Over Monogenic Semigroups, Applied Mathematics and Computation, 322 (2018), 1-5.
  • Y. Nacaroğlu, On the corona product of monogenic semigroup graphs, Adv. and Appl. in Discrete Math., 19(2018) 409-420.
  • Y. Nacaroğlu, On Join Operation of Graphs by Obtained Monogenic Semigroups, Turkish Journal of Mathematics and Computer Science, 13(1)(2021) 57-62.
  • F. Harary, Graph Theory, Addison Wesley, Reading, Mass., 1969.
  • G. A. Bondy, U. S. R. Murty, Graph Teory with Applications, Elsevier Science, New York, NY, USA, (1982).
  • N. Akgüneş, K. C. Das, A. S. Çevik, Topological indices on a graph of monogenic semigroups, Topics in Chemical Graph Theory, 16 (2014), 3-20.
  • B. Aydın, N. Akgüneş, İ. N. Cangül, On the Wiener index of the dot product graph over monogenic semigroups, European Journal of Pure and Applied Mathematics, Vol.13 No.5 (2020), 1231-1240.
  • I. Gutman, O. Polansky, Mathematical Concepts in Organic Chemistry, Springer-Verlag, Berlin, Germany, (1986).
  • D. Plavši´c, S. Nikoli´c, N. Trinajsti´c, Z. Mihali´c, On the Harary index for the characterization of chemical graphs, Journal of Mathematical Chemistry, 12 (1993), 235–250.
  • K. C. Das, K. Xu, I. N. Cangül, A. S. Çevik, A. Graovac, On the Harary index of graph operations, Journal of Inequalities and Applications, vol. 339 (2013).
  • K. Xu, K. C. Das, On harary index of graphs, Discrete Applied Mathematics, vol. 159 no. 15 (2011), 1631–1640.
  • B. H. Xing, G. D. Yu, L. X. Wang, J. Cao, The Harary index of all unicyclic graphs with given diameter, Discrete Dynamics in Nature and Society, (2018).
  • B. Zhou, X. Cai, N. Trinajstic, On Harary Index, Journal of Mathematical Chemistry, 44 (2008), 611-618.
  • S. Pak , Ö. Gürmen Alansal ve U. Cesur , "Pseudo 2- Çaprazlanmış Modüller ve Pseudo 3- Çaprazlanmış Modüller", Necmettin Erbakan Üniversitesi Fen ve Mühendislik Bilimleri Dergisi, 2(2), (2020), 22-37.

Cebirsel Bir Grafın Harary İndeksi

Year 2023, Volume: 5 Issue: 1, 9 - 13, 30.06.2023

Abstract

Topolojik indekslerin matematiksel kimyada kulanım alanı bulunmaktadır. Uzaklık-bazlı topolojik indekslerin ise moleküler graf teoride oldukça önemi vardır. Harary indeksi uzaklık-bazlı bir graf değişmezidir. Yakın zamanda cebirsel bir yapı üzerinde nokta çarpım grafı çalışıldı. Bu çalışmada da bu grafın Harary indeksi verilecektir.

References

  • I. Beck, Coloring of Commutating Ring, Journal of Algebra, 116 (1988), 208-226.
  • D. F. Anderson, P. S. Livingston, The Zero-Divisor Graph of a Commutative Ring, Journal of Algebra, 217 (1999), 434-447.
  • F. R. De Meyer, L. De Meyer, Zero-Divisor Graphs of Semigroups, Journal of Algebra, 283 (2005), 190- 198.
  • A. Badawi, On the Dot Product Graph of a Commutative Ring, Communications in Algebra, 43 (2015), 43-50.
  • K. C. Das, N. Akgüneş, A. S. Çevik, On a Graph of Monogenic Semigroups, Journal of Inequalities and Applications, 2013:44 (2013).
  • N. Akgüneş, B. Çağan, On the Dot Product of Graphs Over Monogenic Semigroups, Applied Mathematics and Computation, 322 (2018), 1-5.
  • Y. Nacaroğlu, On the corona product of monogenic semigroup graphs, Adv. and Appl. in Discrete Math., 19(2018) 409-420.
  • Y. Nacaroğlu, On Join Operation of Graphs by Obtained Monogenic Semigroups, Turkish Journal of Mathematics and Computer Science, 13(1)(2021) 57-62.
  • F. Harary, Graph Theory, Addison Wesley, Reading, Mass., 1969.
  • G. A. Bondy, U. S. R. Murty, Graph Teory with Applications, Elsevier Science, New York, NY, USA, (1982).
  • N. Akgüneş, K. C. Das, A. S. Çevik, Topological indices on a graph of monogenic semigroups, Topics in Chemical Graph Theory, 16 (2014), 3-20.
  • B. Aydın, N. Akgüneş, İ. N. Cangül, On the Wiener index of the dot product graph over monogenic semigroups, European Journal of Pure and Applied Mathematics, Vol.13 No.5 (2020), 1231-1240.
  • I. Gutman, O. Polansky, Mathematical Concepts in Organic Chemistry, Springer-Verlag, Berlin, Germany, (1986).
  • D. Plavši´c, S. Nikoli´c, N. Trinajsti´c, Z. Mihali´c, On the Harary index for the characterization of chemical graphs, Journal of Mathematical Chemistry, 12 (1993), 235–250.
  • K. C. Das, K. Xu, I. N. Cangül, A. S. Çevik, A. Graovac, On the Harary index of graph operations, Journal of Inequalities and Applications, vol. 339 (2013).
  • K. Xu, K. C. Das, On harary index of graphs, Discrete Applied Mathematics, vol. 159 no. 15 (2011), 1631–1640.
  • B. H. Xing, G. D. Yu, L. X. Wang, J. Cao, The Harary index of all unicyclic graphs with given diameter, Discrete Dynamics in Nature and Society, (2018).
  • B. Zhou, X. Cai, N. Trinajstic, On Harary Index, Journal of Mathematical Chemistry, 44 (2008), 611-618.
  • S. Pak , Ö. Gürmen Alansal ve U. Cesur , "Pseudo 2- Çaprazlanmış Modüller ve Pseudo 3- Çaprazlanmış Modüller", Necmettin Erbakan Üniversitesi Fen ve Mühendislik Bilimleri Dergisi, 2(2), (2020), 22-37.
There are 19 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Nihat Akgüneş 0000-0001-7891-2905

Busra Aydın 0000-0002-9450-2938

Publication Date June 30, 2023
Acceptance Date June 21, 2023
Published in Issue Year 2023 Volume: 5 Issue: 1

Cite

APA Akgüneş, N., & Aydın, B. (2023). Harary Index for an Algebraic Graph. Necmettin Erbakan Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi, 5(1), 9-13.
AMA Akgüneş N, Aydın B. Harary Index for an Algebraic Graph. NEJSE. June 2023;5(1):9-13.
Chicago Akgüneş, Nihat, and Busra Aydın. “Harary Index for an Algebraic Graph”. Necmettin Erbakan Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi 5, no. 1 (June 2023): 9-13.
EndNote Akgüneş N, Aydın B (June 1, 2023) Harary Index for an Algebraic Graph. Necmettin Erbakan Üniversitesi Fen ve Mühendislik Bilimleri Dergisi 5 1 9–13.
IEEE N. Akgüneş and B. Aydın, “Harary Index for an Algebraic Graph”, NEJSE, vol. 5, no. 1, pp. 9–13, 2023.
ISNAD Akgüneş, Nihat - Aydın, Busra. “Harary Index for an Algebraic Graph”. Necmettin Erbakan Üniversitesi Fen ve Mühendislik Bilimleri Dergisi 5/1 (June 2023), 9-13.
JAMA Akgüneş N, Aydın B. Harary Index for an Algebraic Graph. NEJSE. 2023;5:9–13.
MLA Akgüneş, Nihat and Busra Aydın. “Harary Index for an Algebraic Graph”. Necmettin Erbakan Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi, vol. 5, no. 1, 2023, pp. 9-13.
Vancouver Akgüneş N, Aydın B. Harary Index for an Algebraic Graph. NEJSE. 2023;5(1):9-13.


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