All 384 pairs of Type-2 isomorphic circulant graphs C_32(R) have been obtained.
Vilfred,A study on Type-2 Isomorphic Circulant Graphs and related Abelian Groups, arXiv: 2012.11372v11 [math.CO] (26 Nov
10 Pith papers cite this work. Polarity classification is still indexing.
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Defines isomorphism series, digraph D, and graph G for circulant graphs C_n(R) and computes them for C_16(R), C_27(S), several C_54 sets, and C_432 while identifying some isomorphisms that are neither Type-1 nor Type-2 w.r.t. m=3.
Computer programs are supplied to generate families of Type-2 isomorphic circulant graphs C_n(R) for m=2,3,5,7 and to demonstrate how Type-1 and Type-2 isomorphisms occur.
V_{n,m}(C_n(R)) forms an Abelian group under ∘ and T2_{n,m}(C_n(R)) is a subgroup, where T2 collects C_n(R) and all its Type-2 isomorphic copies w.r.t. m.
There are 960 triples of Type-2 isomorphic circulant graphs C_54(R) where each triple is Type-2 isomorphic with m=3.
Certain circulant graphs C_16(1,2,7) and C_16(2,3,5) are Type-2 isomorphic w.r.t. m=2, and for n>=2 families C_8n(R) with R={2,2s-1,4n-(2s-1)} and C_8n(S) are Type-2 isomorphic w.r.t. m=2 under stated conditions on n and s.
Two families of circulant graphs C_432(R) and C_6750(S) each possess Type-2 isomorphic variants for two values of m.
Reports 8 pairs of Type-2 isomorphic circulant graphs for order 16, 32 pairs for order 24, and 12 triples for order 27 using a modified definition of Type-2 isomorphism.
Proves that C_{np^3}(R^{np^3,x+yp}_i) for i=1 to p are Type-2 isomorphic w.r.t. m=p and form an Abelian group T2_{np^3,p} under the operation defined by index addition modulo p.
Enumeration yields 18 Type-2 isomorphic pairs for n=48, 72 pairs for n=96, and 27 triples for n=81 among circulant graphs C_n with 3 or 4 generators.
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A study on Type-2 isomorphic circulant graphs. PART 9: Computer programs to show Type-1 $\&$ -2 isomorphic circulant graphs
Computer programs are supplied to generate families of Type-2 isomorphic circulant graphs C_n(R) for m=2,3,5,7 and to demonstrate how Type-1 and Type-2 isomorphisms occur.