2025/08/12 by Kamalappan, Vilfred
#05C25 #05C60 #05C75 #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2508.09384
Circulant graphs Cn(R) and Cn(S) are said to be Adam's isomorphic or \em Type-1 isomorphic if there exist some a∈ ℤn^* such that S = a R under arithmetic reflexive modulo n \citead67. In 1970, Elspas and Turner \citeeltu raised a question on the isomorphism of C16(1,2,7) and C16(2,3,5) and in 1996, Vilfred \citev96 gave its answer by defining Type-2 isomorphism of Cn(R) w.r.t. m \ni m = gcd(n, r) > 1, r∈ R and r,n∈ℕ and studied such graphs for m = 2 in \citev13,v20. Vilfred and Wilson \citevw1 - \citevw3 obtained families of Type-2 isomorphic circulant graphs for m = 3,5,7. In this paper, the author modifies the definition of Type-2 isomorphism of circulant graphs Cn(R) w.r.t. m by considering m > 1 is a divisor of gcd(n, r) and r∈ R and study Type-2 isomorphic circulant graphs of orders 16 and 24. We show that the number of pairs of Type-2 isomorphic circulant graphs of orders 16 and 24 are 8 and 32, respectively and list them all.