Irregular labelings of circulant graphs

We investigate the irregularity strength ( s ( G ) ) and total vertex irregularity strength ( tvs ( G ) ) of circulant graphs C i n ( 1 , 2 , … , k ) and prove that tvs ( C i n ( 1 , 2 , … , k ) ) = ⌈ n + 2 k 2 k + 1 ⌉ , while s ( C i n ( 1 , 2 , … , k ) ) = ⌈ n + 2 k − 1 2 k ⌉ except if either n = 2 k + 1 or if k is odd and n ≡ 2 k + 1 ( mod 4 k ) , then s ( C i n ( 1 , 2 , … , k ) ) = ⌈ n + 2 k − 1 2 k ⌉ + 1 .