Trees with Extreme Values of Second Zagreb Index and Coindex

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Rasi Reza; Sheikholeslami Seyed Mahmoud; Behmaram Afshin

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Journal: Mathematics Interdisciplinary Research Year:2019 | Volume:4 | Issue:2 Page(s): 227-238

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Title

Trees with Extreme Values of Second Zagreb Index and Coindex

Author(s)

Rasi Reza | Sheikholeslami Seyed Mahmoud | Behmaram Afshin | Issue Writer Certificate

Keywords

Zagreb index

second Zagreb index

second Zagreb coindex

tree

Abstract

The second Zagreb indexM2(G) is equal to the sum of the products of the degrees of pairs of adjacent vertices and the second Zagreb coindex M2(G) is equal to the sum of the products of the degrees of pairs of non-adjacent vertices. Kovijanić Vukić ević and Popivoda (Iranian J. Math. Chem. 5 (2014) 19– 29) prove that for any chemical tree of order n 5, M2(T ) 8n − 26 n 0, 1 (mod 3) 8n − 24 otherwise. In this paper we present a generalization of the aforementioned bound for all trees in terms of the order and maximum degree. We also give a lower bound on the second Zagreb coindex of trees.

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APA: Copy

Rasi, Reza, Sheikholeslami, Seyed Mahmoud, & Behmaram, Afshin. (2019). Trees with Extreme Values of Second Zagreb Index and Coindex. MATHEMATICS INTERDISCIPLINARY RESEARCH, 4(2), 227-238. SID. https://sid.ir/paper/745435/en

Vancouver: Copy

Rasi Reza, Sheikholeslami Seyed Mahmoud, Behmaram Afshin. Trees with Extreme Values of Second Zagreb Index and Coindex. MATHEMATICS INTERDISCIPLINARY RESEARCH[Internet]. 2019;4(2):227-238. Available from: https://sid.ir/paper/745435/en

IEEE: Copy

Reza Rasi, Seyed Mahmoud Sheikholeslami, and Afshin Behmaram, “Trees with Extreme Values of Second Zagreb Index and Coindex,” MATHEMATICS INTERDISCIPLINARY RESEARCH, vol. 4, no. 2, pp. 227–238, 2019, [Online]. Available: https://sid.ir/paper/745435/en

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