Comparing the irregularity and the total irregularity of graphs

Darko Dimitrov, Riste Škrekovski

Abstract


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). 


Keywords


The irregularity of graph, the total irregularity of graph, Zagreb indices

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DOI: https://doi.org/10.26493/1855-3974.341.bab

ISSN: 1855-3974

Issues from Vol 6, No 1 onward are partially supported by the Slovenian Research Agency from the Call for co-financing of scientific periodical publications