Graphs with Equal Irregularity Indices

2014 Acta Polytechnica Hungarica  
The irregularity of a graph can be defined by different so-called graph topological indices. In this paper, we consider the irregularities of graphs with respect to the Collatz-Sinogowitz index [8], the variance of the vertex degrees [6], the irregularity of a graph [4], and the total irregularity of a graph [1]. It is known that these irregularity measures are not always compatible. Here, we investigate the problem of determining pairs or classes of graphs for which two or more of the above
more » ... ore of the above mentioned irregularity measures are equal. While in [17] this problem was tackled in the case of bidegreed graphs, here we go a step further by considering tridegreed graphs and graphs with arbitrarily large degree sets. In addition we pressent the smallest graphs for which all above irregularity indices are equal.
doi:10.12700/aph.25.04.2014.04.4 fatcat:w457qtrimvdxremwmke7af3tve