on the harmonic index and harmonic polynomial of caterpillars with diameter four
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abstract
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 caterpillars withf diameter 4.
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Journal title:
iranian journal of mathematical chemistryPublisher: university of kashan
ISSN 2228-6489
volume 6
issue 1 2015
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