پیوندهای مفید
اخبار و اعلانات
آمار
| تعداد نشریات | 11 |
| تعداد شماره‌ها | 210 |
| تعداد مقالات | 2,098 |
| تعداد مشاهده مقاله | 2,878,074 |
| تعداد دریافت فایل اصل مقاله | 2,085,911 |
On linear combinations between Zagreb indices/coindices of a line graph | ||
| Journal of Discrete Mathematics and Its Applications | ||
| دوره 8، شماره 2، مهر 2023، صفحه 63-72 اصل مقاله (276.61 K) | ||
| نوع مقاله: Special Issue: Advances in Combinatorics and Graph Theory: From Algebraic Structures to Real-World Applications | ||
| شناسه دیجیتال (DOI): 10.22061/jdma.2023.9871.1054 | ||
| نویسندگان | ||
| Stefan Stankov؛ Marjan Matejic؛ Igor Milovanovic* ؛ Emina Milovanovic | ||
| Faculty of Electronic Engineering, University of Nis, Nis, Serbia | ||
| تاریخ دریافت: 07 اردیبهشت 1402، تاریخ بازنگری: 13 اردیبهشت 1402، تاریخ پذیرش: 25 اردیبهشت 1402 | ||
| چکیده | ||
| Let $G=(V,E)$, $V=\left\{ v_{1},v_{2},\ldots ,v_{n}\right\}$, be a simple graph of order $n$ and size $m$. Denote by $\Delta = d_1\ge d_2 \ge \cdots \ge d_n= \delta$, $d_i=d(v_i)$, and $\Delta_e=d(e_1)\ge d(e_2)\ge \cdots \ge d(e_m)=\delta_e$, sequences of vertex and edge degrees, respectively. The first reformulated Zagreb index (coindex) is defined as $\displaystyle EM_1(G)=\sum_{i=1}^m d(e_i)^2 = \sum_{e_i\sim e_j}(d(e_i)+d(e_j))$ $\Big(\displaystyle \overline{EM}_1(G) = \sum_{e_i\nsim e_j}(d(e_i)+d(e_j))\Big)$. We consider relationship between reformulated Zagreb indices/coindices and determine their bounds in terms of some basic graph parameters. | ||
| کلیدواژه‌ها | ||
| Topological indices؛ Zagreb indices؛ Line graph | ||
| مراجع | ||
|
[1] A. Ali, I. Gutman, E. Milovanovi´c, I. Milovanovi´c, Sum of powers of the degrees of graphs: extremal results and bounds, MATCH Commun. Math. Comput. Chem. 80 (2018) 5–84. [2] A. R. Ashrafi, T. Doˇsli´c, A. Hamzeh, The Zagreb coindices of graph operations, Discr. Appl. Math. 158 (2010) 1571–1578. [3] B. Bollob´as, P. Erd¨ os, Graphs of extremal weights, Ars Comb. 50 (1998) 225–233. [4] B. Borovi´canin, K. C. Das, B. Furtula, I. Gutman, Bounds for the Zagreb indices,MATCH Commun. Math. Comput. Chem. 78(1) (2017) 17–100. [5] B. Borovi´canin, K. C. Das, B. Furtula, I. Gutman, Zagreb indices: Bounds and extremal graphs, in: I. Gutman, B. Furtula, K. C. Das, E. Milovanovi´c, I. Milovanovi´c (Eds.), Bounds in Chemical Graph Theory – Basics, Univ. Kragujevac, Kragujevac, 2017, 67–153. [6] K. C. Das, Maximizing the sum of the squares of the degrees of a graph, Discr. Math. 285 (2004) 57–66. [7] K. C. Das, Sharp bounds for the sum of the squares of degrees of a graph, Kragujevac J. Math. 25 (2003) 31–49. [8] N. De, Some bounds of reformulated Zagreb indices, Appl. Math. Sci. 6(101) (2012) 5005–5012. [9] T. Doˇsli´c, Vertex–weighted Wiener polynomials for composite graphs, Ars Math. Contemp. 1 (2008) 66–80. [10] M. Gordon, G. J. Scantelbury, Non-random polycondensation: statistical theory of substitution effect, Trans. Farady Soc. 60 (1964) 604–621. [11] I. Gutman, N. Trinajsti´c, Graph theory and molecular orbitals. Total π-electron energy of alternate hydrocarbons, Chem. Phys. Lett. 17(4) (1972) 535–538. [12] I. Gutman, B. Ruˇsˇci´c, N. Trinajsti´c, C. F. Wilcox, Graph theory and molecular orbitals. XII. Acyclic polyenes, J. Chem. Phys. 62 (1975) 3399–3405. [13] I. Gutman, K. Ch. Das, The first Zagreb index 30 years after, MATCH Commun. Math. Comput. Chem. 50 (2004) 83–92. [14] I. Gutman, E. Milovanovi´c, I. Milovanovi´c, Beyond the Zagreb indices, AKCE Int. J. Graphs Comb. 17(1) (2020) 74–85. [15] A. Ili´c, B. Zhou, On reformulated Zagreb indices, Discr. Appl. Math. 160 (2012) 204–209. [16] B. Liu, I. Gutman, Upper bounds for the Zagreb indices of connected graphs, MATCH Commun. Math. Comput. Chem. 55 (2006) 439–446. [17] T. Mansour, M. A. Rostami, E. Suresh, G. B. A. Xavier, New sharp lower bounds for the first Zagreb index, Sci. Publ. State Univ. Novi Pazar, Ser: A, Appl. Math. Inform. Mech. 8 (1) (2016) 11–19. [18] A. Miliˇcevi´c, S. Nikoli´c, N. Trinajsti´c, On reformulated Zagreb indices, Mol. Diversity 8 (2004) 393–399. [19] E. I. Milovanovic´, I. Zˇ . Milovanovic´, E. C´ . Dolic´anin, E. Glogic´, A note on the first reformulated Zagreb index, Appl. Math. Comput. 273 (2016) 16–20. [20] E. I. MIlovanovic´, I. Zˇ . Milovanovic´, Sharp bounds for the first Zagreb index and first Zagreb coindex, Miskolc Math. Notes 16 (2015) 1017–1024. [21] D. S. Mitrinovi´c, P. M. Vasi´c, Analytic inequalities, Springer Verlag, Berlin–Heidelberg–New York, 1970. [22] S. Nikoli´c, G. Kovaˇcevi´c, A. Miliˇcevi´c, N. Trinajsti´c, The Zagreb indices 30 years after, Croat. Chem. Acta 76 (2003) 113–124. [23] K. Pattabiraman, A. Santhakumar, Bounds on first reformulated Zagreb index of graphs, Caspian J. Math. Sci. 7(1) (2018) 25–35. [24] J. R. Platt, Influence of neighbor bonds on additive bond properties in paraffins, J. Chem. Phys. 15 (1947) 419–420. [25] B. Zhou, N. Trinajsti´c, Some properties of the reformulated Zagreb indices, J. Math. Chem. 48 (2010) 714–719. | ||
|
آمار تعداد مشاهده مقاله: 373 تعداد دریافت فایل اصل مقاله: 435 |
||