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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