نشریه علوم ریاضی و انفورماتیک

In this study, we are interested mainly in investigating the relations between two graph irregularity measures which are widely used for structural irregularity characterization of connected graphs. Our study is focused on the comparison and evaluation of the discriminatory ability of irregularity measures called degree deviation S(G) and degree variance V ar(G). We establish various upper bounds for irregularity measures S(G) and V ar(G). It is shown that Nikiforov’s inequality which is valid for connected graphs can be sharpened in the form of V ar(G) < S(G)/2. Among others, it is verified that if G is a bidegreed graph then the discrimination ability of S(G) and V ar(G) is considered to be completely equivalent.