Discrete Mathematics & Theoretical Computer Science, Vol 16, No 1 (2014)

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The Total Irregularity of a Graph

Hosam Abdo, Stephan Brandt, Darko Dimitrov


In this note a new measure of irregularity of a graph G is introduced. It is named the total irregularity of a graph and is defined as irrt(G) = 1 / 2∑u,v ∈V(G) |dG(u)-dG(v)|, where dG(u) denotes the degree of a vertex u ∈V(G). All graphs with maximal total irregularity are determined. It is also shown that among all trees of the same order the star has the maximal total irregularity.

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