A formula with its applications on the difference of Zagreb indices of graphs

Kexiang Xu; Fang Gao; Kinkar Chandra Das; Nenad Trinajstić

doi:10.1007/s10910-019-01025-0

A formula with its applications on the difference of Zagreb indices of graphs

Kexiang Xu, Fang Gao, Kinkar Chandra Das, Nenad Trinajstić

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

26 Scopus citations

Abstract

In this note we focus on the difference ZD₁(G) = M₁(G) - M₂(G) of chemical graphs G where M₁(G) and M₂(G) are first and second Zagreb indices of G, respectively. An explicit formula is obtained for computing the value of ZD₁ of chemical trees with maximum degree 3. As the applications of this formula, we get some results on the properties of ZD₁ of chemical graphs, in particular, we solve the inverse problem for ZD₁ by showing that there is a chemical tree T with ZD₁(T) = t for any integer t∈ (- ∞, 2].

Original language	English
Pages (from-to)	1618-1626
Number of pages	9
Journal	Journal of Mathematical Chemistry
Volume	57
Issue number	6
DOIs	https://doi.org/10.1007/s10910-019-01025-0
State	Published - 15 Jun 2019

Keywords

Chemical tree
Difference of Zagreb indices
Inverse problem

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10.1007/s10910-019-01025-0

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title = "A formula with its applications on the difference of Zagreb indices of graphs",

abstract = "In this note we focus on the difference ZD1(G) = M1(G) - M2(G) of chemical graphs G where M1(G) and M2(G) are first and second Zagreb indices of G, respectively. An explicit formula is obtained for computing the value of ZD1 of chemical trees with maximum degree 3. As the applications of this formula, we get some results on the properties of ZD1 of chemical graphs, in particular, we solve the inverse problem for ZD1 by showing that there is a chemical tree T with ZD1(T) = t for any integer t∈ (- ∞, 2].",

keywords = "Chemical tree, Difference of Zagreb indices, Inverse problem",

author = "Kexiang Xu and Fang Gao and Das, \{Kinkar Chandra\} and Nenad Trinajsti{\'c}",

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doi = "10.1007/s10910-019-01025-0",

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T1 - A formula with its applications on the difference of Zagreb indices of graphs

AU - Xu, Kexiang

AU - Gao, Fang

AU - Das, Kinkar Chandra

AU - Trinajstić, Nenad

PY - 2019/6/15

Y1 - 2019/6/15

N2 - In this note we focus on the difference ZD1(G) = M1(G) - M2(G) of chemical graphs G where M1(G) and M2(G) are first and second Zagreb indices of G, respectively. An explicit formula is obtained for computing the value of ZD1 of chemical trees with maximum degree 3. As the applications of this formula, we get some results on the properties of ZD1 of chemical graphs, in particular, we solve the inverse problem for ZD1 by showing that there is a chemical tree T with ZD1(T) = t for any integer t∈ (- ∞, 2].

AB - In this note we focus on the difference ZD1(G) = M1(G) - M2(G) of chemical graphs G where M1(G) and M2(G) are first and second Zagreb indices of G, respectively. An explicit formula is obtained for computing the value of ZD1 of chemical trees with maximum degree 3. As the applications of this formula, we get some results on the properties of ZD1 of chemical graphs, in particular, we solve the inverse problem for ZD1 by showing that there is a chemical tree T with ZD1(T) = t for any integer t∈ (- ∞, 2].

KW - Chemical tree

KW - Difference of Zagreb indices

KW - Inverse problem

UR - https://www.scopus.com/pages/publications/85064623055

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DO - 10.1007/s10910-019-01025-0

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AN - SCOPUS:85064623055

SN - 0259-9791

VL - 57

SP - 1618

EP - 1626

JO - Journal of Mathematical Chemistry

JF - Journal of Mathematical Chemistry

IS - 6

ER -

A formula with its applications on the difference of Zagreb indices of graphs

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