### The Minimal Total Irregularity of Graphs

#### Abstract

In \cite{2012a}, Abdo and Dimitov defined the total irregularity of a graph $G=(V,E)$ as

\hskip3.3cm $\rm irr_{t}$$(G) = \frac{1}{2}\sum_{u,v\in V}|d_{G}(u)-d_{G}(v)|, $

\noindent where $d_{G}(u)$

denotes the vertex degree of a vertex $u\in V$.

In this paper, we investigate the minimal total irregularity of the connected graphs,

determine the minimal, the second minimal, the third minimal total irregularity of trees, unicyclic graphs, bicyclic graphs on $n$ vertices,

and propose an open problem for further research.

#### Full Text:

PDF### Refbacks

- There are currently no refbacks.