تعداد نشریات | 5 |
تعداد شمارهها | 111 |
تعداد مقالات | 1,247 |
تعداد مشاهده مقاله | 1,199,569 |
تعداد دریافت فایل اصل مقاله | 1,060,288 |
Mathematical results on harmonic polynomials | ||
Communications in Combinatorics and Optimization | ||
مقاله 9، دوره 9، شماره 2، شهریور 2024، صفحه 279-295 اصل مقاله (433.65 K) | ||
نوع مقاله: Original paper | ||
شناسه دیجیتال (DOI): 10.22049/cco.2023.28920.1779 | ||
نویسندگان | ||
Walter Carballosa1؛ J. E. Nápoles2؛ José M. Rodríguez3؛ O. Rosario4؛ José M. Sigarreta* 4 | ||
1Department of Mathematics and Statistics, Florida International University, 11200 SW 8th Street, Miami, FL 33199, USA | ||
2Departamento de Matemáticas, Universidad Nacional de Nordeste, Avenida de la Libertad 5450, 3400 Corrientes, Argentina | ||
3Departamento de Matemáticas, Universidad Carlos III de Madrid, Avenida de la Universidad 30, 28911 Leganés, Madrid, Spain | ||
4Facultad de Matemáticas, Universidad Autónoma de Guerrero, Carlos E. Adame No.54, Col. Garita, 39650 Acalpulco Gro., Mexico | ||
چکیده | ||
The harmonic polynomial was defined in order to understand better the harmonic topological index. Here, we obtain several properties of this polynomial, and we prove that several properties of a graph can be deduced from its harmonic polynomial. Also, we prove that graphs with the same harmonic polynomial share many properties although they are not necessarily isomorphic. | ||
کلیدواژهها | ||
Polynomial؛ Harmonic topological index؛ Graphs | ||
مراجع | ||
[1] B. Borovićanin and B. Furtula, On extremal Zagreb indices of trees with given domination number, Appl. Math. Comput. 279 (2016), 208–218. https://doi.org/10.1016/j.amc.2016.01.017
[2] K.C. Das, On comparing Zagreb indices of graphs, MATCH Commun. Math. Comput. Chem. 63 (2010), no. 2, 433–440.
[3] H. Deng, S. Balachandran, S.K. Ayyaswamy, and Y.B. Venkatakrishnan, On the harmonic index and the chromatic number of a graph, Discrete Appl. Math. 161 (2013), no. 16-17, 2740–2744. https://doi.org/10.1016/j.dam.2013.04.003
[4] Z. Du, B. Zhou, and N. Trinajstić, On the general sum-connectivity index of trees, Appl. Math. Lett. 24 (2011), no. 3, 402–405. https://doi.org/10.1016/j.aml.2010.10.038
[5] M. Eliasi, A. Iranmanesh, and I. Gutman, Multiplicative versions of first Zagreb index, MATCH Commun. Math. Comput. Chem. 68 (2012), no. 1, 217–230.
[6] S. Fajtlowicz, On conjectures of Graffiti-II, Congr. Numer. 60 (1987), 187–197.
[7] G. Fath-Tabar, Zagreb polynomial and Pi indices of some nano structures., Digest J. Nanomat. Biostr. 4 (2009), no. 1, 189–191.
[8] O. Favaron, M. Mahéo, and J.F. Saclé, Some eigenvalue properties in graphs (conjectures of Graffiti–II), Discrete Math. 111 (1993), no. 1-3, 197–220. http://doi.org/10.1016/0012–365X(93)90156–N
[9] B. Furtula and I. Gutman, A forgotten topological index, J. Math. Chem. 53 (2015), no. 4, 1184–1190. https://doi.org/10.1007/s10910-015-0480-z
[10] B. Furtula, I. Gutman, and S. Ediz, On difference of Zagreb indices, Discrete Appl. Math. 178 (2014), 83–88. http://doi.org/10.1016/j.dam.2014.06.011
[11] I. Gutman and B. Furtula, Recent Results in the Theory of Randić Index, Univ. Kragujevac, Kragujevac, 2008.
[12] I. Gutman, B. Furtula, E. Milovanović, and I.Z. Milovanović, Bounds in Chemical Graph Theory-Mainstreams, Mathematical Chemistry Monograph no. 19, Univ. Kragujevac, Kragujevac (Serbia), 2017.
[13] I. Gutman and N. Trinajstić, Graph theory and molecular orbitals. Total $\varphi$-electron energy of alternant hydrocarbons, Chem. Phys. Lett. 17 (1972), no. 4, 535–538. https://doi.org/10.1016/0009-2614(72)85099-1
[14] J.C. Hernández-Gómez, J.A. Méndez-Bermúdez, J.M. Rodríguez, and J.M. Sigarreta, Harmonic index and harmonic polynomial on graph operations, Symmetry 10 (2018), no. 10, Article ID: 456. https://doi.org/10.3390/sym10100456
[15] A. Ilić, Note on the harmonic index of a graph, Ars Combin. 128 (2016), 295–299.
[16] M.A. Iranmanesh and M. Saheli, On the harmonic index and harmonic polynomial of caterpillars with diameter four, Iranian J. Math. Chem. 6 (2015), no. 1, 41–49. https://doi.org/10.22052/ijmc.2015.9044
[17] X. Li, I. Gutman, and M. Randić, Mathematical aspects of Randić-type molecular structure descriptors, Univ. Kragujevac, Kragujevac, 2006.
[18] X. Li and Y. Shi, A survey on the Randić index, MATCH Commun. Math. Comput. Chem. 59 (2008), no. 1, 127–156.
[19] M. Liu, A simple approach to order the first Zagreb indices of connected graphs, MATCH Commun. Math. Comput. Chem. 63 (2010), no. 2, 425–432.
[20] M. Randić, Characterization of molecular branching, J. Am. Chem. Soc. 97 (1975), no. 23, 6609–6615. http://doi.org/10.1021/ja00856a001
[21] J.A. Rodríguez and J.M. Sigarreta, On the Randić index and conditional parameters of a graph, MATCH Commun. Math. Comput. Chem. 54 (2005), no. 2, 403–416.
[22] J.M. Rodríguez and J.M. Sigarreta, New results on the harmonic index and its generalizations, MATCH Commun. Math. Comput. Chem. 78 (2017), no. 2, 387–404.
[23] J.A. Rodríguez-Velázquez and J. Tomás-Andreu, On the Randić index of polymeric networks modelled by generalized Sierpinski graphs, MATCH Commun. Math. Comput. Chem. 74 (2015), no. 1, 145–160.
[24] Y. Shi, M. Dehmer, W. Li, and I. Gutman (eds.), Graph polynomials, series: Discrete mathematics and its applications, Chapman and Hall/CRC, Taylor and Francis Group, Boca Raton, Florida, U.S.A, 2017.
[25] T. Vetrík and M. Abas, Multiplicative Zagreb indices of trees with given domination number, Commun. Comb. Optim. 9 (2024), no. 1, 89–99. https://doi.org/10.22049/cco.2022.27972.1409
[26] H. Wiener, Structural determination of paraffin boiling points, J. Am. Chem. Soc. 69 (1947), no. 1, 17–20. https://doi.org/10.1021/ja01193a005
[27] R. Wu, Z. Tang, and H. Deng, A lower bound for the harmonic index of a graph with minimum degree at least two, Filomat 27 (2013), no. 1, 51–55. https://doi.org/10.2298/FIL1301051W
[28] X. Xu, Relationships between harmonic index and other topological indices, Appl. Math. Sci. 6 (2012), no. 41, 2013–2018.
[29] S. Zafar, R. Nazir, M.S. Sardar, and Z. Zahid, Edge version of harmonic index and harmonic polynomial of some classes of graphs., J. Appl. Math. Inform. 34 (2016), no. 5-6, 479–486. http://doi.org/10.14317/jami.2016.479
[30] L. Zhong and K. Xu, Inequalities between vertex-degree-based topological indices, MATCH Commun. Math. Comput. Chem. 71 (2014), no. 3, 627–642.
[31] B. Zhou and N. Trinajstić, On general sum-connectivity index, J. Math. Chem. 47 (2010), 210–218. https://doi.org/10.1007/s10910-009-9542-4
[32] Z. Zhu and H. Lu, On the general sum-connectivity index of tricyclic graphs, J. Appl. Math. Comput. 51 (2016), 177–188. http://doi.org/10.1007/s12190-015-0898-2 | ||
آمار تعداد مشاهده مقاله: 352 تعداد دریافت فایل اصل مقاله: 719 |