THE ZAGREB INDICES OF BIPARTITE GRAPHS WITH MORE EDGES |
XU, KEXIANG
(Department of Mathematics, College of Science, Nanjing University of Aeronautics & Astronautics)
TANG, KECHAO (Department of Mathematics, College of Science, Nanjing University of Aeronautics & Astronautics) LIU, HONGSHUANG (Department of Mathematics, College of Science, Nanjing University of Aeronautics & Astronautics) WANG, JINLAN (Department of Mathematics, College of Science, Nanjing University of Aeronautics & Astronautics) |
1 | M. Eliasi, A. Iranmanesh and I. Gutman, Multiplicative versions of first Zagreb index, MATCH Commun. Math. Comput. Chem. 68 (2012), 217-230. |
2 | I. Gutman, Multiplicative Zagreb indices of trees, Bulletin of Society of Mathematicians Banja Luka 18 (2011), 17-23. |
3 | A.R. Ashrafi, T. Došlić and A. Hamzeh, The Zagreb coindices of graph operations, Discrete Appl. Math. 158 (2010), 1571-1578. DOI |
4 | R. Todeschini and V. Consonni, Zagreb indices (Mn), in: Molecular descriptors for chemoinformatics, Wiley-VCH, Weinheim, I(2009), 955-966. |
5 | 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. |
6 | N. Trinajstić, Chemical Graph Theory, CRC Press, Boca Raton, FL, 1992. |
7 | K. Xu, The Zagreb indices of graphs with a given clique number, Appl. Math. Lett. 24 (2011), 1026-1030. DOI |
8 | K. Xu and K.C. Das, Trees, unicyclic, and bicyclic graphs extremal with respect to multi-plicative sum Zagreb index, MATCH Commun. Math. Comput. Chem. 68 (2012), 257-272. |
9 | K. Xu, K.C. Das and K. Tang, On the multiplicative Zagreb coindex of graphs, Opuscula Math. 33 (2013), 197-210. |
10 | K. Xu, K.C. Das and S. Balachandran, Maximizing the Zagreb indices of (n,m)- graphs, MATCH Commun. Math. Comput. Chem. 72 (2014), 641-654. |
11 | K. Xu and 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. |
12 | I. Gutman and K.C. Das, The first Zagreb index 30 years after, MATCH Commun. Math. Comput. Chem. 50 (2004), 83-92. |
13 | I. Gutman and O.E. Polansky, Mathematical Concepts in Organic Chemistry, Springer, Berlin, 1986. |
14 | I. Gutman and N. Trinajstić, Graph theory and molecular orbitals. III. Total π-electron energy of alternant hydrocarbons, Chem. Phys. Lett. 17 (1972), 535-538. DOI |
15 | I. Gutman, B. Ruščić, N. Trinajstić and C.F. Wilcox, Graph theory and molecular orbitals. XII. Acyclic polyenes, J. Chem. Phys. 62 (1975), 3399-3405. DOI |
16 | B. Lučić, S. Nikolić and N. Trinajstić, Zagreb indices, in: Chemical information and computational challenges in the 21st century, edited by M.V. Putz, Nova Sci. Publ. New York, 2012, 261-275. |
17 | S. Nikolić, G. Kovačević, A. Miličević and N. Trinajstić, The Zagreb indices 30 years after, Croat. Chem. Acta 76 (2003), 113-124. |
18 | R. Todeschini, D. Ballabio and V. Consonni, Novel molecular descriptors based on func-tions of new vertex degrees, In: Novel molecular structure descriptors - Theory and applications I. (I. Gutman, B. Furtula, eds.), pp. 73-100. Kragujevac: Univ. Kragujevac 2010. |
19 | I. Gutman, Degree-based topological indices, Croat. Chem. Acta 86 (2013), 351-361. DOI |
20 | R. Todeschini and V. Consonni, Handbook of Molecular Descriptors, Wiley-VCH, Weinheim, 2000. |
21 | I. Gutman, An exceptional property of first Zagreb index, MATCH Commun. Math. Comput. Chem. 72 (2014) 733-740. |
22 | A.R. Ashrafi, T. Došlić and A. Hamzeh, Extremal graphs with respect to the Zagreb coindices, MATCH Commun. Math. Comput. Chem. 65 (2011), 85-92. |
23 | A.T. Balaban, I. Motoc, D. Bonchev and O. Mekenyan, Topological indices for structure- activity corrections, Topics Curr. Chem. 114 (1983), 21-55. DOI |
24 | J.A. Bondy and U.S.R. Murty, Graph Theory with Applications, Macmillan Press, New York, 1976. |
25 | K.C. Das, Maximizing the sum of the squares of degrees of a graph, Discrete Math. 257 (2004), 57-66. DOI |
26 | K.C. Das, N. Akgünes, M. Togan, A. Yurttas, I.N. Cangül and A.S. Cevik, On the first Za-greb index and multiplicative Zagreb coindices of graphs, Analele Stiintifice ale Universitatii Ovidius Constanta, in press. |
27 | K.C. Das, I. Gutman and B. Zhou, New upper bounds on Zagreb indices, J. Math. Chem. 46 (2009), 514-521. DOI |
28 | K.C. Das and I. Gutman, Some properties of the second Zagreb index, MATCH Commun. Math. Comput. Chem. 52 (2004), 103-112. |
29 | H. Deng, A unified approach to the extremal Zagreb indices for trees, unicyclic graphs and bicyclic graphs, MATCH Commun. Math. Comput. Chem. 57 (2007), 597-616. |
30 | T. Došlić, Vertex-weighted Wiener polynomials for composite graphs, Ars Math. Contemp. 1 (2008), 66-80. |