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In 1972 , Gutman and Trinajestic presented first Zagreb index M1 and the second Zagreb index M2. For a given connected graph G, which is equal to the first point M1 Zagreb degree indicator squares , Zagreb index M2 is equal to the second neighboring point , and the product of the degree . For a connected graph G, an [DM Cvetkoci'c, M. Doob and H. Sachs, Spectra of Graphs-Theory and Applications, Academic Press, New York, 1980] defines the five kinds of graph G associated with the mesh operation , defined as L (G), S (G), R (G), Q (G) , and T (G). recently, [M. Eliasi, B. Taeri, Four new sums of graphs and their Wiener indices, Discr. Appl. Math. 157 (2009) 794-803] , the use of the back four figure shows the F-sums FIG Wiener definitions and their targets. In [MHKhalifeh, H. Yousefi-Azari, AR Ashrafi, SG Wagner, Some new results on distance-based graph invariants, European J. Comb. 30 (2009) 1149-1163] in , Khalifeh et al. Gives the diagram computing the two graphs Cartesian product , composition, join, disjunction and symmetric di? erence of the first and second Zagreb indices exact formulas . In this paper , we split the relevant figure , F-sums diagram and IV product (Kronecker product , strong plot , skew product and converse skew product ) figure first and second Zagreb index were studied.
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