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The harmonic index of subdivision graphs | ||
| Transactions on Combinatorics | ||
| مقاله 2، دوره 6، شماره 4، اسفند 2017، صفحه 15-27 اصل مقاله (270.89 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/toc.2017.21471 | ||
| نویسنده | ||
| Bibi Naimeh Onagh* | ||
| Golestan University | ||
| چکیده | ||
| The harmonic index of a graph $G$ is defined as the sum of the weights $\frac{2}{\deg_G(u)+\deg_G(v)}$ of all edges $uv$ of $G$, where $\deg_G(u)$ denotes the degree of a vertex $u$ in $G$. In this paper, we study the harmonic index of subdivision graphs, $t$-subdivision graphs and also, $S$-sum and $S_t$-sum of graphs. | ||
| کلیدواژهها | ||
| harmonic index؛ subdivision؛ $S$-sum؛ inverse degree؛ Zagreb index | ||
| مراجع | ||
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[1] A. Astaneh-Asl and G. H. Fath-Tabar, Computing the rst and third Zagreb p olynomials of Cartesian pro duct of graphs, Iranian J. Math. Chem., 2 no. 2 (2011) 73-78.
[2] P. S. Bullen, A dictionary of inequalities, Addison-Wesley Longman, 1998.
[3] H. Deng, S. Balachandran, S. K. Ayyaswamy and Y. B. Venkatakrishnan, On the harmonic index and the chromatic numb er of a graph, Discrete Appl. Math., 161 (2013) 2740-2744.
[4] M. Eliasi and B. Taeri, Four new sums of graphs and their Wiener indices, Discrete Appl. Math., 157 (2009) 794-803.
[5] S. Fa jtlowicz, On conjectures of graffiti I I, Congr. Numer., 60 (1987) 189-197.
[6] G. H. Fath-Tabar, Old and new Zagreb indices of graphs, MATCH Commun. Math. Comput. Chem., 65 (2011) 79-84.
[7] A. Ilic, M. Ilic and B. Liu, On the upp er b ounds for the rst Zagreb index, Kragujevac J. Math., 35 (2011) 173-182.
[8] J. Li, J. B. Lv and Y. Liu, The harmonic index of some graphs, Bul l. Malays. Math. Sci. Soc., 39 (2016) 331-340.
[9] J. B. Lv and J. Li, On the harmonic index and the matching numb ers of trees, Ars Combin., 116 (2014) 407-416.
[10] J. B. Lv, J. Li and W. C. Shiu, The harmonic index of unicyclic graphs with given matching number, Kragujevac J. Math., 38 (2014) 173-182.
[11] S. Nikolic, G. Kovacevic, A. Milicevic and N. Trina jstic, The Zagreb indices 30 years after, Croat. Chem. Acta, 76 (2003) 113-124.
[12] B. N. Onagh, The harmonic index of pro duct graphs, Math. Sci., (2017) 1-7.
[13] B. N. Onagh, The harmonic index of edge-semitotal graphs, total graphs and related sums, Kragujevac J. Math., to app ear.
[14] B. N. Onagh, The harmonic index for R-sum of graphs, submitted.
[15] B. S. Shwetha, V. Lokesha and P. S. Ranjini, On the harmonic index of graph op erations, Trans. Comb. , 4 no. 4 (2015) 5-14.
[16] R. Wu, A. Tang and H. Deng, A lower b ound for the harmonic index of a graph with minimum degree at least two, Filomat, 27 (2013) 51-55.
[17] X. Xu, Relationships b etween harmonic index and other top ological indices, Appl. Math. Sci., 6 (2012) 2013-2018.
[18] L. Zhong, The harmonic index for graphs, Appl. Math. Lett., 25 (2012) 561-566.
[19] L. Zhong, The harmonic index on unicyclic graphs, Ars Combin., 104 (2012) 261-269.
[20] L. Zhong, On the harmonic index and the girth for graphs, Rom. J. Inf. Sci. Tech., 16 no. 4 (2013) 253-260.
[21] L. Zhong and K. Xu, The harmonic index for bicyclic graphs, Utilitas Math., 90 (2013) 23-32.
[22] L. Zhong and K. Xu, Inequalities b etween vertex-degree-based top ological indices, MATCH Commun. Math. Com-put. Chem., 71 (2014) 627-642. | ||
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