in this paper, the hyper - zagreb index of the cartesian product, composition and corona product of graphs are computed. these corrects some errors in g. h. shirdel et al.[11].

the atom bond connectivity index of a graph is a new topological index was defined by e.estrada as abc(g)  uve (dg(u) dg(v) 2) / dg(u)dg(v) , where g d ( u ) denotes degreeof vertex u. in this paper we present some bounds of this new topological index.

the harmonic index h(g) , of a graph g is defined as the sum of weights 2/(deg(u)+deg(v)) of all edges in e(g), where deg (u) denotes the degree of a vertex u in v(g). in this paper we define the harmonic polynomial of g. we present explicit formula for the values of harmonic polynomial for several families of specific graphs and we find the lower and upper bound for harmonic index in caterpill...

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in the conventional design and analysis methods affecting parameters (loads, materials'strength, etc) are not set as probable variables. safety factors in the current codes andstandards are usually obtained on the basis of judgment and experience, which may beimproper or uneconomical. in technical literature, a method based on nonlinear static analysisis suggested to set reliability index on st...

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