For i € {1,2} and T e {T,}, assume that G, are connected gra and edge set E(T(G,)) is happened after operating phs and the graph 7(G,) having vertex set V(T(G,)) the operations T on G,. Then, the graphs G, +, G, having ver if for (a,,b,)(a,,b,) € E(G, +, G,) either a, = a, in V bb, €E(G,) or b, = b, in V(G,) and aa, € E(S(G,)), and car and edge set E(G, +, G,) are called T-sum gra esian product is the best fitted and the most sty ex set V(G, +, G,) = V(T(G,)) x (V,) = (V, U E) x phs G,) nas n presented according to cartesian product because ish apparatus to construct a large network from a simple gra ph and is also important for designing as wel as exploration of networks (Xu, 2001). For more clearance, see Figures 2 and 3. FIGURE 8: (a) 3D plot of M,(@,) and M,(,) are labbled in red and blue graphs, (b) 3D plot of ZC,(0,) and ZC,(6,) are labbled in green and purple graphs, (c) 3D plot of ZC, (8, ), iad (6, ) and ZC (6, ) are labbled in golden, ferozi and riehroort graphs, ‘d) 3D plot of M,(6,) and M_(0, are labbled in red and blue graphs, (e) 3D plot of ZC. ‘(oy ) and ZC. (6, ) are labbled in green and purple graphs, (f) 3D plot of ZC, (6, ), ZC, (6, and ZC, (6, ) are labbled in golden, ferozi and mehroon graphs Figure 9: (a) 3D plot of M,(6,), M,(@,), ZC,(@,), ZC,(6,), ZC, (0,), ZC, (6), and ZC, (6, are labbled in blue, red, purple, green, orange, gray and mehroon graphs, (b) 3D plot of M,(@,), M,(@,), ZC,(6,), ZC,(9,), ZC, (6,), ZC, (6,), and ZC, (6,) are labbled in blue, red, green, purple, orange, gray, and mehroon graphs Table 1: Numeric comparison of the indicated Zagreb indices related to 7,-operation. 4.1 Comparisons with 3D plots Table 2: Numeric comparison of the indicated Zagreb indices related to T,-operation. Table 3: Different values of C.V of the indicated Zagreb indices for both operations 7, and T,. References Table 4: Different values of X of the indicated Zagreb indices for both operations 7, and T,. Figure 10: Graph for C.V of the indicated ZI’s for both operations T, and T, based on Table 3 Figure 11: Graph for arithmetic mean (A.M) of the indicated ZI’s for both operations based on Table 4
