Harary Index for an Algebraic Graph
Year 2023,
Volume: 5 Issue: 1, 9 - 13, 30.06.2023
Nihat Akgüneş
,
Busra Aydın
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
Nihat Akgüneş
,
Busra Aydın
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.