Irregular labelings of circulant graphs

We investigate the irregularity strength (s(G)) and total vertex irregularity strength (tvs(G)) of circulant graphs Ci(n)(1, 2, ... , k) and prove that tvs(Ci(n) (1, 2, ... , k)) = inverted right perpendicularn+2k/2k+1inverted left perpendicular, while s(Ci(n)(1, 2, ... , k)) = inverted right perpendicularn+2k-1/2kinverted left perpendicular except if either n = 2k + 1 or if k is odd and n 2k + 1(mod 4k), then s(Ci(n) (1, 2, ... , k)) = inverted right perpendicularn-2k-1/2kinverted left perpendicular + 1. (C) 2012 Elsevier B.V. All rights reserved.