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.
Vilfred Kamalappan,New Families of Circulant Graphs Without Cayley Isomorphism Property withr i = 2, Int
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.
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.
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A study on Type-2 isomorphic circulant graphs. Part 7: Isomorphism series, digraph and graph of $C_n(R)$
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.
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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 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 8: $C_{432}(R)$, $C_{6750}(S)$ -- each has 2 types of Type-2 isomorphic circulant graphs
Two families of circulant graphs C_432(R) and C_6750(S) each possess Type-2 isomorphic variants for two values of m.
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A study on Type-2 isomorphic circulant graphs. Part 2: Type-2 isomorphic circulant graphs of orders 16, 24, 27
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.