Irregular labelings of circulant graphs

AbstractWe investigate the irregularity strength (s(G)) and total vertex irregularity strength (tvs(G)) of circulant graphs Cin(1,2,…,k) and prove that tvs(Cin(1,2,…,k))=⌈n+2k2k+1⌉, while s(Cin(1,2,…,k))=⌈n+2k−12k⌉ except if either n=2k+1 or if k is odd and n≡2k+1(mod4k), then s(Cin(1,2,…,k))=⌈n+2k−12k⌉+1