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- W1792309686 abstract "Albertson has defined the irregularity of a simple undirected graph $G=(V,E)$ as $ irr(G) = sum_{uvin E}|d_G(u)-d_G(v)|,$ where $d_G(u)$ denotes the degree of a vertex $u in V$. Recently, this graph invariant gained interest in the chemical graph theory, where it occured in some bounds on the first and the second Zagreb index, and was named the third Zagreb index Fath-Tabar. For general graphs with $n$ vertices, Albertson has obtained an asymptotically tight upper bound on the irregularity of $4 n^3 /27.$ Here, by exploiting a different approach than in Albertson, we show that for general graphs with $n$ vertices the upper bound $lfloor frac{n}{3} rfloor lceil frac{2 n}{3} rceil (lceil frac{2 n}{3} rceil -1)$ is sharp. Next, we determine $k$-cyclic graphs with maximal irregularity. We also present some bounds on the maximal/minimal irregularity of graphs with fixed minimal and/or maximal vertex degrees, and consider an approximate computation of the irregularity of a graph." @default.
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- W1792309686 date "2012-07-19" @default.
- W1792309686 modified "2023-10-02" @default.
- W1792309686 title "Bounds and Computation of Irregularity of a Graph" @default.
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