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On trees and the multiplicative sum Zagreb index | ||
| Communications in Combinatorics and Optimization | ||
| مقاله 4، دوره 1، شماره 2، اسفند 2016، صفحه 137-148 اصل مقاله (727.17 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2016.13574 | ||
| نویسندگان | ||
| Mehdi Eliasi* 1؛ Ali Ghalavand2 | ||
| 1Dept. of Mathematics, Khansar Faculty of Mathematics and Computer Science, Khansar, Iran, | ||
| 2Dept. of Mathematics, Khansar Faculty of Mathematics and Computer Science, Khansar, Iran | ||
| چکیده | ||
| For a graph $G$ with edge set $E(G)$, the multiplicative sum Zagreb index of $G$ is defined as $\Pi^*(G)=\Pi_{uv\in E(G)}[d_G(u)+d_G(v)]$, where $d_G(v)$ is the degree of vertex $v$ in $G$. In this paper, we first introduce some graph transformations that decrease this index. In application, we identify the fourteen class of trees, with the first through fourteenth smallest multiplicative sum Zagreb indices among all trees of order $n\geq 13$. | ||
| کلیدواژهها | ||
| Multiplicative Sum Zagreb Index؛ Graph Transformation؛ Branching Point؛ trees | ||
| مراجع | ||
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[1] M. Azari and A. Iranmanesh, Some inequalities for the multiplicatiove sum zagreb index of graph operations, J Math. Inequal. 9 (2015), 727–738.
[2] A. T. Balaban, I. Motoc, D. Bonchev, and O. Mekenyan, Topological indices for structure-activity correlations, Topics Curr. Chem. 114 (1983), 21–55.
[3] C. Bey, An upper bound on the sum of squares of degrees in a hypergraph, Discrete Math. 269 (2003), 259–263.
[4] K.C. Das, Sharp bounds for the sum of the squares of the degrees of a graph, Kragujevac J. Math. 25 (2003), 31–49.
[5] D. de Caen, An upper bound on the sum of squares of degrees in a graph, Discrete Math. 185 (1998), 245–248.
[6] M. Eliasi, A. Iranmanesh, and I. Gutman, Multiplicative versions of first zagreb index, MATCH Commun. Math. Comput. Chem. 68 (2012), 217–230.
[7] M. Eliasi and D. Vukicević, Comparing the multiplicative zagreb indices, MATCH Commun. Math. Comput. Chem. 69 (2013), 765–773.
[8] I. Gutman, Graphs with smallest sum of squares of vertex degrees, MATCH Commun. Math. Comput. Chem. 25 (2003), 51–54.
[9] I. Gutman and K. C. Das, The first zagreb index 30 years after, MATCH Commun. Math. Comput. Chem. 50 (2004), 83–92.
[10] I. Gutman and N. Trinajstić, Graph theory and molecular orbitals. total p-electron energy of alternant hydrocarbons, Chem. Phys. Lett. 17 (1972), 535–538.
[11] S. Nikolić, G. Kovacević, Milićević, and A. N. Trinajstić, The zagreb indices 30 years after, Croat. Chem. Acta 76 (2003), 113–124.
[12] R. Todeschini, D. Ballabio, and V. Consonni, Novel molecular descriptors based on functions of new vertex degrees. in:i. gutman and b. furtula (eds.), novel molecular structure descriptors-theory and applicationsi, Univ. Kragujevac (2010), 73–100.
[13] R. Todeschini and V. Consonni, Handbook of molecular descriptors, WileyVCH Weinheim, 2000.
14] R. Todeschini and V. Consonni, New local vertex invariants and molecular descriptors based on functions of the vertex degrees, MATCH Commun. Math. Comput. Chem. 64 (2010), 359–372.
[15] H. Wang and H. Bao, A note on multiplicative sum zagreb index, South Asian J. Math. 2 (2012), 578–583.
[16] K. Xu, Trees with the seven smallest and eight greatest harary indices, Discrete Appl. Math. 160 (2012), 321–331.
[17] K. Xu and K. Das, Trees, unicyclic and bicyclic graphs extremal with respect to multiplicative sum zagreb index, MATCH Commun. Math. Comput. Chem. 68 (2012), 257–272.
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