### The Total Irregularity of a Graph

*Hosam Abdo, Stephan Brandt, Darko Dimitrov*

#### Abstract

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 irr_{t}(G) = 1 / 2∑_{u,v ∈V(G)}|d_{G}(u)-d_{G}(v)|, where d_{G}(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.Full Text: PDF PostScript