Multiplicative Zagreb indices and coindices of some derived graphs

• Autorzy: Basavanagoud B. , Patil S.

Identyfikatory

DOI

10.7494/OpMath.2016.36.3.287

• Języki publikacji: EN

Abstrakty

EN

In this note, we obtain the expressions for multiplicative Zagreb indices and coindices of derived graphs such as a line graph, subdivision graph, vertex-semitotal graph, edge-semitotal graph, total graph and paraline graph.

Słowa kluczowe

EN

multiplicative Zagreb indices and coindices; derived graphs

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2016
• Tom: Vol. 36, no. 3
• Strony: 287--299
• Opis fizyczny: Bibliogr. 20 poz., rys.

Twórcy

autor

Basavanagoud B.

• Karnatak University Department of Mathematics Dharwad - 580 003, Karnataka, India

autor

Patil S.

• Karnatak University Department of Mathematics Dharwad - 580 003, Karnataka, India

Bibliografia

• [1] M. Azari, A. Iranmanesh, Some inequalities for the multiplicative sum Zagreb index of graph operations, Journal of Mathematical Inequalities 9 (2015) 3, 727-738.
• [2] B. Basavanagoud, I. Gutman, V.R. Desai, Zagreb indices of generalized transformation graphs and their complements, Kragujevac J. Sci. 37 (2015), 99-112.
• [3] B. Basavanagoud, I. Gutman, C.S. Gali, On second Zagreb index and coindex of some derived graphs, Kragujevac J. Sci. 37 (2015), 113-121.
• [4] K.C. Das, A. Yurttas, M. Togan, A.S. Cevik, I.N. Cangul, The multiplicative Zagreb indices of graph operations, Journal of Inequality and Applications (2013), 2013:90.
• [5] M. Eliasi, A. Iranmanesh, I. Gutman, Multiplicative versions of first Zagreb index, MATCH Commun. Math. Comput. Chem. 68 (2012), 217-230.
• [6] I. Gutman, Multiplicative Zagreb indices of trees, Bull. Internat. Math. Virt. Inst. 1 (2011), 13-19.
• [7] I. Gutman, Degree-based topological indices, Croat. Chem. Acta 86 (2013), 351-361.
• [8] I. Gutman, B. Furtula, Ž. Kovijanić Vukićević, G. Popivoda, Zagreb indices and coindices, MATCH Commun. Math. Comput. Chem. 74 (2015), 5-16.
• [9] F. Harary, Graph Theory, Addison-Wesley, Reading, Mass 1969.
• [10] J. Liu, Q. Zhang, Sharp upper bounds for multiplicative Zagreb indices, MATCH Commun. Math. Comput. Chem. 68 (2012), 231-240.
• [11] H. Narumi, M. Katayama, Simple topological index. A newly devised index characterizing the topological nature of structural isomers of saturated hydrocarbons, Mem. Fac. Engin. Hokkaido Univ. 16 (1984), 209-214.
• [12] T. Réti, I. Gutman, Relations between ordinary and multiplicative Zagreb indices, Bull. Internat. Math. Virt. Inst. 2 (2012), 133-140.
• [13] R. Todeschini, 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.
• [14] R. Todeschini, D. Ballabio, V. Consonni, Novel molecular descriptors based on functions of new vertex degrees, [in:] I. Gutman, B. Furtula (eds), Novel molecular structure descriptors - Theory and applications I, Univ. Kragujevac, 2010, 73-100.
• [15] Ž. Tomovič, I. Gutman, Narumi-Katayama index of phenylenes, J. Serb. Chem. Sco. 66 (2001) 4, 243-247.
• [16] H. Wang, H. Bao, A note on multiplicative sum Zagreb index, South Asian J. Math. 2 (2012) 6, 578-583.
• [17] S. Wang, B. Wei, Multiplicative Zagreb indices of k-tree, Discrete Applied Math. 180 (2015), 168-175.
• [18] 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.
• [19] K. Xu, K.C. Das, K. Tang, On the multiplicative Zagreb coindex of graphs, Opuscula Math. 33 (2013) 1, 191-204.
• [20] 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.

Uwagi

PL

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.