Leap Zagreb indices of trees and unicyclic graphs

Gutman, Ivan; Shao, Zehui; Li, Zepeng; Wang, ShaohuiShaohui; We, Pu

doi:10.22049/cco.2018.26285.1092

تعداد نشریات	5
تعداد شماره‌ها	111
تعداد مقالات	1,247
تعداد مشاهده مقاله	1,199,486
تعداد دریافت فایل اصل مقاله	1,060,191

	Leap Zagreb indices of trees and unicyclic graphs
Communications in Combinatorics and Optimization
مقاله 6، دوره 3، شماره 2، اسفند 2018، صفحه 179-194 اصل مقاله (434.37 K)
نوع مقاله: Original paper
شناسه دیجیتال (DOI): 10.22049/cco.2018.26285.1092
نویسندگان
Ivan Gutman^* ¹؛ Zehui Shao²؛ Zepeng Li³؛ ShaohuiShaohui Wang⁴؛ Pu We⁵
¹University of Kragujevac
²Guangzhou University
³Lanzhou University
⁴Department of Mathematics and Computer Science, Adelphi University, Garden City, NY, USA.
⁵Guangzhou University,
چکیده
By $d(v\|G)$ and $d_2(v\|G)$ are denoted the number of first and second neighbors of the vertex $v$ of the graph $G$. The first, second, and third leap Zagreb indices of $G$ are defined as $LM_1(G) = \sum_{v \in V(G)} d_2(v\|G)^2$, $LM_2(G) = \sum_{uv \in E(G)} d_2(u\|G)\,d_2(v\|G)$, and $LM_3(G) = \sum_{v \in V(G)} d(v\|G)\,d_2(v\|G)$, respectively. In this paper, we generalize the results of Naji et al. [Commun. Combin. Optim. {\bf 2} (2017), 99--117], pertaining to trees and unicyclic graphs. In addition, we determine upper and lower bounds on these leap Zagreb indices and characterize the extremal graphs.
کلیدواژه‌ها
Leap Zagreb index؛ Zagreb index؛ degree (of vertex)

مراجع
[1] A. Ali and N. Trinajstić, A novel/old modification of the first zagreb index, Mol. Inf. 37 (2018), no. 6/7, Article ID: 1800008. [2] B. Borovicanin, K.C. Das, B. Furtula, and I. Gutman, Bounds for Zagreb indices, MATCH Commun. Math. Comput. Chem 78 (2017), no. 1, 17–100. [3] J.C. Dearden, The Use of Topological Indices in QSAR and QSPR Modeling, Advances in QSAR Modeling, Springer, Cham, 2017, pp. 57–88. [4] J. Devillers and A.T. Balaban (Eds.), Topological Indices and Related Descriptors in QSAR and QSPAR, Gordon & Breach, Amsterdam, 2000. [5] I. Gutman, E. Milovanović, and I. Milovanović, Beyond the zagreb indices, AKCE Int. J. Graphs Combin. (2018), in press. [6] I. Gutman, B. Ruščić, N. Trinajstić, and C.F. Wilcox, Graph theory and molecular orbitals. XII. acyclic polyenes, J. Chem. Phys. 62 (1975), no. 9, 3399–3405. [7] I. Gutman and N. Trinajstić, Graph theory and molecular orbitals. Total ϕelectron energy of alternant hydrocarbons, Chem. Phys. Lett. 17 (1972), no. 4, 535–538. [8] A.M. Naji and N.D. Soner, The first leap zagreb index of some graph opertations, Int. J. Appl. Graph Theory 2 (2018), no. 2, 7–18. [9] A.M. Naji, N.D. Soner, and I. Gutman, The first leap zagreb index of some graph opertations, Commun. Comb. Optim. 2 (2017), no. 2, 99–117. [10] N.D. Soner and A.M. Naji, The k-distance neighborhood polynomial of a graph, Int. J. Math. Comput. Sci. 3 (2016), no. 9, 2359–2364. [11] R. Todeschini and V. Consonni, Molecular Descriptors for Chemoinformatics, Wiley–VCH, Weinheim, 2009. [12] S. Yamaguchi, Estimating the zagreb indices and the spectral radius of triangleand quadrangle-free connected graphs, Chem. Phys. Lett. 458 (2008), no. 4-6, 396–398.
آمار تعداد مشاهده مقاله: 1,191 تعداد دریافت فایل اصل مقاله: 1,003

سامانه مدیریت نشریات علمی. قدرت گرفته از سیناوب

پیوندهای مفید

آمار

Leap Zagreb indices of trees and unicyclic graphs