Geodesic
Comparing the irregularity and the total irregularity of graphs
Ars Mathematica Contemporanea, Tome 9 (2015) no. 1, pp. 45-50.

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Albertson has defined the irregularity of a simple undirected graph G as irr(G) = ∑ uv ∈ E(G)∣dG(u) − dG(v)∣,  where dG(u) denotes the degree of a vertex u ∈ V(G). Recently, in  a new measure of irregularity of a graph, so-called the total irregularity, was defined as irrt(G) = 1/2 ∑ u, v ∈ V(G)∣dG(u) − dG(v)∣.  Here, we compare the irregularity and the total irregularity of graphs. For a connected graph G with n vertices, we show that irrt(G) ≤ n2irr(G) / 4.  Moreover, if G is a tree, then irrt(G) ≤ (n − 2)irr(G).
DOI : 10.26493/1855-3974.341.bab
Keywords: The irregularity of graph, the total irregularity of graph, Zagreb indices 
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Darko Dimitrov; Riste Škrekovski. Comparing the irregularity and the total irregularity of graphs. Ars Mathematica Contemporanea, Tome 9 (2015) no. 1, pp. 45-50. doi : 10.26493/1855-3974.341.bab. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.341.bab/

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