On comparing Zagreb indices of graphs

Batmend Horoldagva; Kinkar C. Das

On comparing Zagreb indices of graphs

Batmend Horoldagva
, Kinkar C. Das

Department of Mathematics

Mongolian National University of Education

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

25 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. It is well-known that for connected or disconnected graphs, M₂/m ≥ M₁/n does not hold always. In K.C. Das (On comparing Zagreb indices of graphs, MATCH Commun. Math. Comput. Chem. 63, 433-440, 2010), it has been shown that the above relation holds for a special kind of graph. Here we continue our search for special kinds of graph for which the above relation holds.

Original language	English
Pages (from-to)	223-230
Number of pages	8
Journal	Hacettepe Journal of Mathematics and Statistics
Volume	41
Issue number	2
State	Published - Apr 2012

Keywords

Cartesian product
First Zagreb index
Second Zagreb index
Threshold graph

Cite this

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title = "On comparing Zagreb indices of graphs",

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. It is well-known that for connected or disconnected graphs, M2/m ≥ M1/n does not hold always. In K.C. Das (On comparing Zagreb indices of graphs, MATCH Commun. Math. Comput. Chem. 63, 433-440, 2010), it has been shown that the above relation holds for a special kind of graph. Here we continue our search for special kinds of graph for which the above relation holds.",

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AU - Das, Kinkar C.

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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. It is well-known that for connected or disconnected graphs, M2/m ≥ M1/n does not hold always. In K.C. Das (On comparing Zagreb indices of graphs, MATCH Commun. Math. Comput. Chem. 63, 433-440, 2010), it has been shown that the above relation holds for a special kind of graph. Here we continue our search for special kinds of graph for which the above relation holds.

KW - Cartesian product

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KW - Second Zagreb index

KW - Threshold graph

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On comparing Zagreb indices of graphs

Abstract

Keywords

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