×

The Zagreb coindices of graph operations. (English) Zbl 1201.05100

Summary: Recently introduced Zagreb coindices are a generalization of classical Zagreb indices of chemical graph theory. We explore here their basic mathematical properties and present explicit formulae for these new graph invariants under several graph operations.

MSC:

05C90 Applications of graph theory
05C07 Vertex degrees
92E10 Molecular structure (graph-theoretic methods, methods of differential topology, etc.)
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Ashrafi, A.R.; Došlić, T.; Hamzeh, A., Extremal graphs with respect to the Zagreb coindices, MATCH commun. math. comput. chem., 65, 85-92, (2011) · Zbl 1265.05135
[2] Das, K.Ch.; Gutman, I., Some properties of the second Zagreb index, MATCH commun. math. comput. chem., 52, 103-112, (2004) · Zbl 1077.05094
[3] Diudea, M.V.; Gutman, I.; Jantschi, L., Molecular topology, (2001), Huntington NY
[4] Došlić, T., Vertex-weighted Wiener polynomials for composite graphs, Ars math. contemp., 1, 66-80, (2008) · Zbl 1163.05012
[5] Došlić, T., Splices, links, and their degree-weighted Wiener polynomials, Graph theory notes N. Y., XLVIII, 47-55, (2005)
[6] Graovac, A.; Pisanski, T., On the Wiener index of a graph, J. math. chem., 8, 53-62, (1991)
[7] Harary, F., Graph theory, (1969), Addison-Wesley Reading MA · Zbl 0797.05064
[8] Imrich, W.; Klavžar, S., Product graphs: structure and recognition, (2000), John Wiley & Sons New York
[9] Khalifeh, M.H.; Yousefi-Azari, H.; Ashrafi, A.R.; Gutman, I., The edge Szeged index of product graphs, Croat. chem. acta, 81, 277-281, (2008)
[10] Khalifeh, M.H.; Yousefi-Azari, H.; Ashrafi, A.R., Vertex and edge PI indices of Cartesian product graphs, Discrete appl. math., 156, 1780-1789, (2008) · Zbl 1152.05323
[11] Khalifeh, M.H.; Yousefi-Azari, H.; Ashrafi, A.R., The first and second Zagreb indices of graph operations, Discrete appl. math., 157, 804-811, (2009) · Zbl 1172.05314
[12] Khalifeh, M.H.; Yousefi-Azari, H.; Ashrafi, A.R.; Wagner, S., Some new results on distance-based graph invariants, European J. combin., 30, 1149-1163, (2009) · Zbl 1189.05054
[13] Khalifeh, M.H.; Yousefi-Azari, H.; Ashrafi, A.R., The hyper-Wiener index of graph operations, Comput. math. appl., 56, 1402-1407, (2008) · Zbl 1155.05316
[14] Khalifeh, M.H.; Yousefi-Azari, H.; Ashrafi, A.R., A matrix method for computing Szeged and vertex PI indices of join and composition of graphs, Linear algebra appl., 429, 2702-2709, (2008) · Zbl 1156.05034
[15] Klavžar, S., On the PI index: PI-partitions and Cartesian product graphs, MATCH commun. math. comput. chem., 57, 573-586, (2007) · Zbl 1142.05317
[16] Klavžar, S.; Rajapakse, A.; Gutman, I., The Szeged and the Wiener index of graphs, Appl. math. lett., 9, 45-49, (1996) · Zbl 0903.05020
[17] Klein, D.J.; Došlić, T.; Bonchev, D., Vertex-weightings for distance moments and thorny graphs, Discrete appl. math., 155, 2294-2302, (2007) · Zbl 1127.05030
[18] Nikolić, S.; Kovačević, G.; Miličević, A.; Trinajstić, N., The Zagreb indices 30 years after, Croat. chem. acta, 76, 113-124, (2003)
[19] Sagan, B.E.; Yeh, Y.-N.; Zhang, P., The Wiener polynomial of a graph, Int. J. quant. chem., 60, 959-969, (1996)
[20] Stevanović, D., Hosoya polynomials of composite graphs, Discrete math., 235, 237-244, (2001) · Zbl 0973.05026
[21] Todeschini, R.; Consoni, V., Handbook of molecular descriptors, (2002), Wiley-VCH New York
[22] Trinajstić, N., Chemical graph theory, (1992), CRC Press Boca Raton, FL
[23] West, D.B., Introduction to graph theory, (1996), Prentice Hall Upper Saddle River · Zbl 0845.05001
[24] Yousefi-Azari, H.; Manoochehrian, B.; Ashrafi, A.R., The PI index of product graphs, Appl. math. lett., 21, 624-627, (2008) · Zbl 1149.05015
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.