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Comparing Zagreb Indices of Cyclic Graphs (CROSBI ID 163591)

Prilog u časopisu | izvorni znanstveni rad | međunarodna recenzija

Caporossi, Gillese ; Hansen, Piere ; Vukičević, Damir Comparing Zagreb Indices of Cyclic Graphs // MATCH : communications in mathematical and in computer chemistry, 63 (2010), 2; 441-451

Podaci o odgovornosti

Caporossi, Gillese ; Hansen, Piere ; Vukičević, Damir

engleski

Comparing Zagreb Indices of Cyclic Graphs

Given a graph G=(V, E), the first Zagreb index M₁ is the sum of its vertices squared degrees and the second Zagreb index M₂ is the sum of its edges products of degrees. Recently, there has been much interest in comparing M₁ and M₂ (and generalizations of them). The case of trees was handled in <cite>vukicevic08</cite>. In this paper, we consider the case of cyclic graphs and provide two best possible lower bounds on M₂-M₁ in terms of order and cyclicity of G. On the basis of some experiments with the system AutoGraphiX, it was conjectured that M₁/n≤M₂/m. This was disproved in <cite>hansen07</cite> both for disconnected and for connected graphs. However, it is true for chemical graphs. We show here that it still holds for unicyclic graphs but is not true in general for graphs with a larger number of independent cycles.

Zagreb index; cyclic graph

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Podaci o izdanju

63 (2)

2010.

441-451

objavljeno

0340-6253

Povezanost rada

Kemija, Matematika

Indeksiranost