The Ratio and Product of the Multiplicative Zagreb Indices

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KAZEMI RAMIN

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Journal Paper

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Journal: Iranian Journal of Mathematical Chemistry Year:2017 | Volume:8 | Issue:4 Page(s): 377-390

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Title

The Ratio and Product of the Multiplicative Zagreb Indices

Author(s)

KAZEMI RAMIN | Issue Writer Certificate

Keywords

molecular graph with tree structureQ1

multiplicative Zagreb indexQ1

momentQ1

Doob’s supermartingale inequalityQ1

Abstract

The first multiplicative Zagreb index  1(G) is equal to the product of squares of the degree of the vertices and the second multiplicative Zagreb index  2(G) is equal to the product of the products of the degree of pairs of adjacent vertices of the underlying molecular graphs G. Also, the multiplicative sum Zagreb index  3(G) is equal to the product of the sums of the degree of pairs of adjacent vertices of G. In this paper, weintroduce a new version of the multiplicative sum Zagreb index and study the moments of the ratio and product of all indices in a randomly chosen molecular graph with tree structure of order n. Also, a supermartingale is introduced by Doob’ s supermartingale inequality.

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APA: Copy

KAZEMI, RAMIN. (2017). The Ratio and Product of the Multiplicative Zagreb Indices. IRANIAN JOURNAL OF MATHEMATICAL CHEMISTRY, 8(4 ), 377-390. SID. https://sid.ir/paper/205513/en

Vancouver: Copy

KAZEMI RAMIN. The Ratio and Product of the Multiplicative Zagreb Indices. IRANIAN JOURNAL OF MATHEMATICAL CHEMISTRY[Internet]. 2017;8(4 ):377-390. Available from: https://sid.ir/paper/205513/en

IEEE: Copy

RAMIN KAZEMI, “The Ratio and Product of the Multiplicative Zagreb Indices,” IRANIAN JOURNAL OF MATHEMATICAL CHEMISTRY, vol. 8, no. 4 , pp. 377–390, 2017, [Online]. Available: https://sid.ir/paper/205513/en

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