Minimal spread of integral circulant graphs

The integral circulant graph ICGn(D) has the vertex set Z(n)= {0,1,2,...,n-1} and vertices a and b are adjacent if gcd(a-b,n)is an element of D, whereD subset of {d:d|n,1 <= d<n}.In this paper we prove that the minimal value of the spread of the integral circulant graphs ICG(n)(D) of a given order n with its prime factorizationp alpha 11<middle dot><middle dot><middle dot>p alpha kk, is equal to & sum;ki=1p alpha ii-1 or & sum;ki=1p alpha ii, depending on whethern=2<middle dot>3<middle dot>p alpha 33<middle dot><middle dot><middle dot>p alpha kkor not, respectively. Furthermore, we completely characterize all graphs whose minimal spread attains the mentioned values in the class of connected integral circulant graphs of a given order. (c) 2023 Published by Elsevier B.V.