Some Topological Indices and ( Hosoya and Schultz) Polynomial of Subgroup intersection graph of a group Z_r
DOI:
https://doi.org/10.29304/jqcm.2021.13.1.757Keywords:
Subgroup Intersection graph of a group, Eccentric connectivity index, connectivity index, Sum connectivity index, Forgotten index, Geometric index, Harmonic index, Hosoya Polynomial, Schultz PolynomialAbstract
Let be any group with identity element (e) . A subgroup intersection graph of a group is the Graph with V (G) = - e and two separate a vertices a and b contiguous for a and b if and only if , Where is a cyclic subgroup of generated by . We found some topological indices in this paper and (Hosoya and Schultz) Polynomial of , where , is a prime number.
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References
[1] M.R. Darafsheh , " Computation of topological indices of some graphs," Acta Appl .Math., vol.110, no.3,pp.1225-1235,(2010).
[2] A. IIic, G.Yu ,and L. Feng ,ˮ On the eccentric distance sum of graphs ,ˮ J. Math .Anal .Appl., vol.381,pp.590-600,(2011).
[3] M. Azari and A. Iranmanesh , ˮComputing the eccentric-distance sum for graph operations ,ˮ Discret .Appl.Math., vol.161,no. 18,pp.2827-2840,(2013).
[4] P.Padmapriya and V.Mathad, ˮThe eccentric-distance sum of some graphs ,ˮ Electron .J. Graph theory Appl.,vol.5,no.1,pp.51-62,(2017).
[5] Morgan M.J., Mukwembi S. and Swart H.C. ˮOn the eccentric Connectivity index of Graghˮ , Discrete Mathematics , 311(2011), 1229-1234, (2009).
[6] Abdelgader M.S., Wang C. and Mohamed S.A. ˮ Computation of Topological indices of some Special Graphs ˮ , mathematics , 6(33), (2018).
[7] Kinkar Ch.D,Das S. and Zkou B. ˮ Sum-connectivity index of Gragh ˮ, Frontiers of mathematics in china , 11(1),47-54, (2016).
[8]B. Zhou and N. Trinajstic ,"On a novel connectivity index ,"J. Math .Chem., vol.46,no.4,pp.1252-1270,(2009).
[9]B. Lucic , N. Trinajstic ,and B. Zhou," Comparison between the sum-connectivity index and product-connectivity index for benzenoid hydrocarbons,"Chem.Phys.lett.,vol.475,no.1-3,pp.146-148,(2009).
[10]B. Zhou and N. Trinajstic ,"On general sum-connectivity index,"J.Math.Chem.,vol.47,no.1,pp.210-218,(2010).
[11] Khalifeh M.H., Yousefi- Azari H. and Ashrafi A.R . ˮThe first and second Zagrab indices of some Gragh operationsˮ , Discrete applied mathematics , 157,(2009), 804-811,(2008).
[12]I.Gutman,"Degree-based topological indices,"Croat.Chem.Acta,vol.86,no.4,pp.351-361,(2014).
[13]I.Gutman,E.Milovanovic,and I.Milovanovic, "Beyond the Zagreb indices,"AKCE Int.J.Graphs Commb,(2018).
[14]R . Rasi , S. M. Sheikholeslami ,and A. Behmaram , "An upper bound on the first Zagreb index in trees,"Iran.J.Math.Chemstry,vol.8,no.1,pp.71-82,(2017).
[15]T.Doslic, "Vertex-weighted Winer polynomials for composite graphs ," Ars Math.Contep.,vol.1,no.1,pp.66-80,(2008).
[16]B.Furtula,I. Gutman ,and S. Ediz ,"On difference of Zagreb indices,"Discret.Appl.Math., vol.178,pp.83-88,(2014).
[17]R.Ksazemi and A.Behotei,"The first Zagreb and forgotten topological indices of d-ary trees,"Hacettepe J.Math.Stat.,vol46,no.4,pp.603-612,(2017).
[18] B.Futula and I.Gutman,"Aforgotten topological index," J.Math.Chem.,vol.53,no.4,pp.1184-1190,(2015).
[19]S.Akhter,M.Imran, and M.R.Farahani, "Extremal unicyclic and bicyclic graphs with respect to the F-index,"AKCE Int.J.Graphs Comb., vol .14,no.1,pp.80-91,(2017).
[20] Khaksari A. and Ghorbani M. , ˮ The Forgotten Topological index ˮ ,Iranian Journal of mathematical chemistry , 8(3),327-338,(2017).
[21] Abdelgader M.S., Wang C. and Mohamed S.A. ˮComputation of Topological indices of some Special Graphs ˮ , mathematics , 6(33), (2018).
[22]K.C.Das,I. Gutman,and B.furtula,"On the first geometric-arithmetic index of graphs,"Discret.Appl.Math.,vol.159,no.17,pp.2030-2037,(2017).
[23]W.Gao and W.F.Wang," The fifth geometric-arithmetic index of bridge graph and carbon nanocones ," J. Differ. Equations Appl.,vol.23,no.1-2,pp.100-109,(2017).
[24] Zhong L. ˮThe Harmonic index for Graghsˮ , applied mathematics letters ,25(3),561-566, (2012).
[25]L.Zhong and K.Xu,"The harmonic index for bicyclic graphs,"Util.Math.,vol.90,(2013).
[26]J.Liu,"On the harmonic index of triangle-free graphs,"Appl.Math.,vol.04,no.08,pp.1204-1206,(2013).
[27]J.Li and W.C.Shiu,"The harmonic index of a graph ,"Rocky Mt.J.Math.,vol.5,pp.1607-1620,(2014).
[28] T.Tamizh Chelvam and M.Sattanathan (2011) ,. ˮ Subgroup intersection graph of a group ˮ .J . Adv. Research in pure Math (doi: 10.5373/ jarpm . 594.100910 , issN:1943-2380).3(4),44-49
[29] Mohammed.S.A,(2020) "Representation of some Group and Rings in Graph Theory with study some of it's properties for topological indices", M. Sc. Thesis, Mosul University.
[30]Abdussakir .,"Some Topological Indices of Subgroup Graph of Symmetric Group", Mathematics and Statistics 7(4):98-105,(2019).
[31]G.R.Roshini,"Some Degree Based Topological Indices of Transformation Graphs", Bull. Int. Math .Virtual Inst., vol. 10(2)(2020),225-237.
[32]Chang-Cheng Wei "Some Topological Invariants of Graph Associated with the Group of Symmetries ", volume 2020,Article ID 6289518,13 pages.
[33] Hosoya H.,(1985),״ On Some Counting Polynomials in Chemistry ״
[34]Chartrand, G. and Lesniak . Graph and Diagraphs , 6th ed ., Wadsworth and Brooks/Cole . California. (2016).
[35] Gutman ״Selected properties of the Schultz molecular Topological index״ .J. Chem. Inf. Comput . Sci. 34, pp. 1087-1089,(1994).
[2] A. IIic, G.Yu ,and L. Feng ,ˮ On the eccentric distance sum of graphs ,ˮ J. Math .Anal .Appl., vol.381,pp.590-600,(2011).
[3] M. Azari and A. Iranmanesh , ˮComputing the eccentric-distance sum for graph operations ,ˮ Discret .Appl.Math., vol.161,no. 18,pp.2827-2840,(2013).
[4] P.Padmapriya and V.Mathad, ˮThe eccentric-distance sum of some graphs ,ˮ Electron .J. Graph theory Appl.,vol.5,no.1,pp.51-62,(2017).
[5] Morgan M.J., Mukwembi S. and Swart H.C. ˮOn the eccentric Connectivity index of Graghˮ , Discrete Mathematics , 311(2011), 1229-1234, (2009).
[6] Abdelgader M.S., Wang C. and Mohamed S.A. ˮ Computation of Topological indices of some Special Graphs ˮ , mathematics , 6(33), (2018).
[7] Kinkar Ch.D,Das S. and Zkou B. ˮ Sum-connectivity index of Gragh ˮ, Frontiers of mathematics in china , 11(1),47-54, (2016).
[8]B. Zhou and N. Trinajstic ,"On a novel connectivity index ,"J. Math .Chem., vol.46,no.4,pp.1252-1270,(2009).
[9]B. Lucic , N. Trinajstic ,and B. Zhou," Comparison between the sum-connectivity index and product-connectivity index for benzenoid hydrocarbons,"Chem.Phys.lett.,vol.475,no.1-3,pp.146-148,(2009).
[10]B. Zhou and N. Trinajstic ,"On general sum-connectivity index,"J.Math.Chem.,vol.47,no.1,pp.210-218,(2010).
[11] Khalifeh M.H., Yousefi- Azari H. and Ashrafi A.R . ˮThe first and second Zagrab indices of some Gragh operationsˮ , Discrete applied mathematics , 157,(2009), 804-811,(2008).
[12]I.Gutman,"Degree-based topological indices,"Croat.Chem.Acta,vol.86,no.4,pp.351-361,(2014).
[13]I.Gutman,E.Milovanovic,and I.Milovanovic, "Beyond the Zagreb indices,"AKCE Int.J.Graphs Commb,(2018).
[14]R . Rasi , S. M. Sheikholeslami ,and A. Behmaram , "An upper bound on the first Zagreb index in trees,"Iran.J.Math.Chemstry,vol.8,no.1,pp.71-82,(2017).
[15]T.Doslic, "Vertex-weighted Winer polynomials for composite graphs ," Ars Math.Contep.,vol.1,no.1,pp.66-80,(2008).
[16]B.Furtula,I. Gutman ,and S. Ediz ,"On difference of Zagreb indices,"Discret.Appl.Math., vol.178,pp.83-88,(2014).
[17]R.Ksazemi and A.Behotei,"The first Zagreb and forgotten topological indices of d-ary trees,"Hacettepe J.Math.Stat.,vol46,no.4,pp.603-612,(2017).
[18] B.Futula and I.Gutman,"Aforgotten topological index," J.Math.Chem.,vol.53,no.4,pp.1184-1190,(2015).
[19]S.Akhter,M.Imran, and M.R.Farahani, "Extremal unicyclic and bicyclic graphs with respect to the F-index,"AKCE Int.J.Graphs Comb., vol .14,no.1,pp.80-91,(2017).
[20] Khaksari A. and Ghorbani M. , ˮ The Forgotten Topological index ˮ ,Iranian Journal of mathematical chemistry , 8(3),327-338,(2017).
[21] Abdelgader M.S., Wang C. and Mohamed S.A. ˮComputation of Topological indices of some Special Graphs ˮ , mathematics , 6(33), (2018).
[22]K.C.Das,I. Gutman,and B.furtula,"On the first geometric-arithmetic index of graphs,"Discret.Appl.Math.,vol.159,no.17,pp.2030-2037,(2017).
[23]W.Gao and W.F.Wang," The fifth geometric-arithmetic index of bridge graph and carbon nanocones ," J. Differ. Equations Appl.,vol.23,no.1-2,pp.100-109,(2017).
[24] Zhong L. ˮThe Harmonic index for Graghsˮ , applied mathematics letters ,25(3),561-566, (2012).
[25]L.Zhong and K.Xu,"The harmonic index for bicyclic graphs,"Util.Math.,vol.90,(2013).
[26]J.Liu,"On the harmonic index of triangle-free graphs,"Appl.Math.,vol.04,no.08,pp.1204-1206,(2013).
[27]J.Li and W.C.Shiu,"The harmonic index of a graph ,"Rocky Mt.J.Math.,vol.5,pp.1607-1620,(2014).
[28] T.Tamizh Chelvam and M.Sattanathan (2011) ,. ˮ Subgroup intersection graph of a group ˮ .J . Adv. Research in pure Math (doi: 10.5373/ jarpm . 594.100910 , issN:1943-2380).3(4),44-49
[29] Mohammed.S.A,(2020) "Representation of some Group and Rings in Graph Theory with study some of it's properties for topological indices", M. Sc. Thesis, Mosul University.
[30]Abdussakir .,"Some Topological Indices of Subgroup Graph of Symmetric Group", Mathematics and Statistics 7(4):98-105,(2019).
[31]G.R.Roshini,"Some Degree Based Topological Indices of Transformation Graphs", Bull. Int. Math .Virtual Inst., vol. 10(2)(2020),225-237.
[32]Chang-Cheng Wei "Some Topological Invariants of Graph Associated with the Group of Symmetries ", volume 2020,Article ID 6289518,13 pages.
[33] Hosoya H.,(1985),״ On Some Counting Polynomials in Chemistry ״
[34]Chartrand, G. and Lesniak . Graph and Diagraphs , 6th ed ., Wadsworth and Brooks/Cole . California. (2016).
[35] Gutman ״Selected properties of the Schultz molecular Topological index״ .J. Chem. Inf. Comput . Sci. 34, pp. 1087-1089,(1994).
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Published
2021-02-25
How to Cite
Nawaf, A. J., & Mohammad, A. S. (2021). Some Topological Indices and ( Hosoya and Schultz) Polynomial of Subgroup intersection graph of a group Z_r. Journal of Al-Qadisiyah for Computer Science and Mathematics, 13(1), Math Page 120– 130. https://doi.org/10.29304/jqcm.2021.13.1.757
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