Comparing Zagreb Indices of Cyclic Graphs (CROSBI ID 163591)
Prilog u časopisu | izvorni znanstveni rad | međunarodna recenzija
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