Relationship between the eccentric connectivity index and Zagreb indices

Kinkar Ch Das; N. Trinajstić

doi:10.1016/j.camwa.2011.06.017

Relationship between the eccentric connectivity index and Zagreb indices

Kinkar Ch Das, N. Trinajstić

Department of Mathematics

Ruder Boskovic Institute

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

27 Scopus citations

Abstract

For a (molecular) graph, the first Zagreb index M₁ is equal to the sum of the squares of the degrees of the vertices, and the second Zagreb index M₂ is equal to the sum of the products of the degrees of pairs of adjacent vertices. If G is a connected graph with vertex set V(G), then the eccentric connectivity index of G, ξ^C(G), is defined as, ∑_vi∈V(G)^diei, where ^di is the degree of a vertex ^vi and ^ei is its eccentricity. In this report we compare the eccentric connectivity index (ξ^C) and the Zagreb indices (M₁ and M₂) for chemical trees. Moreover, we compare the eccentric connectivity index (ξ^C) and the first Zagreb index (M₁) for molecular graphs.

Original language	English
Pages (from-to)	1758-1764
Number of pages	7
Journal	Computers and Mathematics with Applications
Volume	62
Issue number	4
DOIs	https://doi.org/10.1016/j.camwa.2011.06.017
State	Published - Aug 2011

Keywords

Chemical tree
Eccentric connectivity index (ξ)
First Zagreb index (M)
Molecular graph
Second Zagreb index (M)

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10.1016/j.camwa.2011.06.017

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abstract = "For a (molecular) graph, the first Zagreb index M1 is equal to the sum of the squares of the degrees of the vertices, and the second Zagreb index M2 is equal to the sum of the products of the degrees of pairs of adjacent vertices. If G is a connected graph with vertex set V(G), then the eccentric connectivity index of G, ξC(G), is defined as, ∑vi∈V(G)diei, where di is the degree of a vertex vi and ei is its eccentricity. In this report we compare the eccentric connectivity index (ξC) and the Zagreb indices (M1 and M2) for chemical trees. Moreover, we compare the eccentric connectivity index (ξC) and the first Zagreb index (M1) for molecular graphs.",

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AU - Trinajstić, N.

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AB - For a (molecular) graph, the first Zagreb index M1 is equal to the sum of the squares of the degrees of the vertices, and the second Zagreb index M2 is equal to the sum of the products of the degrees of pairs of adjacent vertices. If G is a connected graph with vertex set V(G), then the eccentric connectivity index of G, ξC(G), is defined as, ∑vi∈V(G)diei, where di is the degree of a vertex vi and ei is its eccentricity. In this report we compare the eccentric connectivity index (ξC) and the Zagreb indices (M1 and M2) for chemical trees. Moreover, we compare the eccentric connectivity index (ξC) and the first Zagreb index (M1) for molecular graphs.

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KW - Eccentric connectivity index (ξ)

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KW - Second Zagreb index (M)

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Relationship between the eccentric connectivity index and Zagreb indices

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