en عمومى General پژوهشي Research paper <p style="text-align: justify;">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&rsquo;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.</p> <s(g) 2.="" a="" ability="" among="" bidegreed="" discrimination="" g="" graph="" if="" is="" it="" of="" others="" s="" that="" the="" then="" verified=""></s(g)> Irregularity measure, Degree deviation, Degree variance, Bidegreed graph. 85 105 http://ijmsi.ir/browse.php?a_code=A-10-6995-1&slc_lang=en&sid=1 Ali Ghalavand alighalavand@grad.kashanu.ac.ir 100319475328460012030 100319475328460012030 Yes Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan 87317-53153, I. R. Iran Tamás Réti reti.tamas@bgk.uni-obuda.hu 100319475328460012031 100319475328460012031 No Donát Bánki Faculty of Mechanical and Safety Engineering, Óbudá University, Népszínház u. 8, H-1081, Budapest, Hungary Igor Z. Milovanović igor.milovanovic@elfak.ni.ac.rs 100319475328460012032 100319475328460012032 No Faculty of Electronic Engineering, Nis, Serbia Ali Reza Ashrafi ashrafi@kashanu.ac.ir 100319475328460012033 100319475328460012033 No Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan 87317-53153, I. R. Iran