All 384 pairs of Type-2 isomorphic circulant graphs C_32(R) have been obtained.
Vilfred Kamalappan,A study on Type-2 Isomorphic Circulant Graphs and related Abelian Groups, arXiv: 2012.11372v11 [math.CO] (26 Nov
5 Pith papers cite this work. Polarity classification is still indexing.
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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.
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 3: 384 pairs of Type-2 isomorphic circulant graphs $C_{32}(R)$
All 384 pairs of Type-2 isomorphic circulant graphs C_32(R) have been obtained.
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A study on Type-2 isomorphic circulant graphs. Part 6: Abelian groups $(T2_{n,m}(C_n(R)), \circ)$ and $(V_{n,m}(C_n(R)), \circ)$
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.
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A study on Type-2 isomorphic circulant graphs. Part 4: 960 triples of Type-2 isomorphic circulant graphs $C_{54}(R)$
There are 960 triples of Type-2 isomorphic circulant graphs C_54(R) where each triple is Type-2 isomorphic with m=3.
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A study on Type-2 isomorphic circulant graphs. Part 1: Type-2 isomorphic circulant graphs $C_n(R)$ w.r.t. $m$ = 2
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.
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A study on Type-2 isomorphic circulant graphs. Part 5: Type-2 isomorphic circulant graphs of orders 48, 81, 96
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.