Leap Zagreb Indices of Some Graph Operations
محورهای موضوعی : مجله بین المللی ریاضیات صنعتی
N. Dehgardi
1
(
Department of Mathematics and Computer Science, Sirjan University of Technology Sirjan, Iran.
)
R. Khoeilar‎
2
(
Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran.
)
M. Soroudi
3
(
Department of Mathematics
Azarbaijan Shahid Madani University
Tabriz, Iran
)
کلید واژه: Zagreb indices, Consumers., Supply chains, Leap Zagreb indices, Graph operations,
چکیده مقاله :
The fiirst leap Zagreb index of a graph, is the sum of squares of the second degrees of vertices (number of their second neighbors), and the second leap Zagreb index is the sum of the products of the second degrees of pairs of adjacent vertices, and the third leap Zagreb index is the sum of the product of the degree and second degree of the vertices.
شاخص اول زاگرب جهشی (مولکولار) گراف برابر مجموع مربعات دومین درجه راس‌ها، شاخص دوم زاگرب جهشی، مجموع حاصلضرب زوج راس‌های مجاور دومین درجه‌ها و شاخص سوم زاگرب جهشی، مجموع حاصلضرب درجه و دومین درجه‌ها می‌باشند. در این مقاله، ما به بررسی عملگر‌های برخی گراف‌ها برای اولین، دومین و سومین شاخص‌های زاگرب جهشی می‌پردازیم.
[1] H. Aram, N. Dehgardi, Reformulated Findex of graph operations, Commun. Comb. Optim, 2 (2017) 87-98.
[2] H. Aram, N. Dehgardi, A. Khodkar, The third ABC index of some graph operations, Bull. Int. Combin. Math. Appl. 78 (2016) 69-82.
[3] A. Ashrafi, T. Doˇ sli´ c, A. Hamzeh, The Zagreb coindices of graph operations, Discrete Appl. Math 158 (2010) 1571-1578.
[4] B. Basavanagoud, S. Patil, A note on hyperzagreb index of graph operations, Iran. J. Math. Chem. 7 (2016) 89-92.
[5] B. Borovicanin, K.C. Das, B. Furtula, I. Gutman, Bounds for Zagreb indices, MATCH Commun. Math. Comput. Chem 78 (2017) 17-100.
[6] K.C. Das, I. Gutman, Some properties of the second Zagreb index, MATCH Commun. Math. Comput. Chem 52 (2004) 103-112.
[7] K.C. Das, I. Gutman, The first Zagreb index 30 years after, MATCH Commun. Math. Comput. Chem 50 (2004) 83-92.
[8] K.C. Das, A Yurttas, M. Togan, A. S. Cevik, and I.N. Cangul, The multiplicative Zagreb indices of graph operations,J. Inequal. Appl. (2013), http://dx.doi.org/10.1186/1029-242X-2013-90/.
[9] N. Dehgardi, A note on revised Szeged index of graph operations, Iranian J. Math. Chem. 9 (2018) 57-63.
[10] T. Doˇ sli´ c, Vertex-weighted Wiener polynomials for composite graphs, Ars Math. Contemp. 1 (2008) 66-80.
[11] M. Eliasi, A. Iranmanesh, I. Gutman, Multiplicative versions of first zagreb index, MATCH Commun. Math. Comput. Chem. 68 (2012) 217-230.
[12] M. Eliasi, G. Raeisi, B. Taeri, Wiener index of some graph operations, Discrete Appl. Math. 160 (2012) 1333-1344.
[13] I. Gutman, Multiplicative zagreb indices of trees, Bull. Soc. Math. Banja Luka 18 (2011) 17-23.
[14] I. Gutman, B. Furtula, K. Vuki´ cevi´ c, G. Popivoda, On Zagreb indices and coindices, MATCH Commun. Math. Comput. Chem 74 (2015) 5-16.
[15] I. Gutman, N. Trinajsti´ c, Graph theory and molecular orbitals. total π-electron energy of alternant hydrocarbons, Chem. Phys. Lett 17 (1972) 535-538.
[16] I. Gutman, B. Rucˇ ciˇ c, N. Trinajsti´ c, C. F. Wilcox, Graph theory and molecular orbitals, XII. acyclic polyenes, J. Chem. Phys. 62 (1975) 3399-3405.
[17] A. Ili´ c, B. Zhou, On reformulated zagreb indices, Discrete Appl. Math. 160 (2012) 204-209.
[18] M. H. Khalifeh, H. Yousefi-Azari, A. R. Ashrafi, The hyper-Wiener index of graph operations, Comput. Math. Appl. 56 (2008) 1402-1407.
[19] M. H. Khalifeh, H. Yousefi-Azari, A. R. Ashrafi, The first and second Zagreb indices of some graph operations, Discrete Appl. Math. 157 (2009) 804-811.
[20] A. Miliˇ cevi´ c, S. Nikoli´ c, N. Trinajsti´ c, On reformulated zagreb indices, Mol. Diversity 8 (2004) 393-399.
[21] A. M. Naji, N. D. Soner, Ivan Gutman, On leap Zagreb indices of graphs, Commun. Comb. Optim 2 (2017) 99-117.
[22] S. Nikoli´ c, G. Kovaˇ cevi´ c, A. Miliˇ cevi´ c, N. Trinajsti´ c, The Zagreb indices 30 years after, Croat. Chem. Acta 76 (2003) 113-124.
[23] K. Pattabiraman, M. Vijayaragavan, Hyper zagreb indices and its coindices of graphs, Bull. Int. Math. Virt. Inst. 7 (2017) 31-41.
[24] K. Xu, K. C. Das, Trees, unicyclic, and bicyclic graphs extremal with respect to multiplicative sum zagreb index, MATCH Commun. Math. Comput. Chem. 68 (2012) 257-272.
[25] K. Xu, K. C. Das, K. Tang, On the multiplicative zagreb coindex of graphs, Opuscula Math. 33 (2013) 191-204.
[26] K. Xu, H. Hua, A unified approach to extremal multiplicative zagreb indices for trees, unicyclic and bicyclic graphs, MATCH Commun. Math. Comput. Chem. 68 (2012) 241-256.
