On isomorphic factorizations of circulant graphs (original) (raw)
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2017 7th International Conference on Modeling, Simulation, and Applied Optimization (ICMSAO), 2017
We present different properties of circulant graphs that includes (i) On the existence of self-complementary circulant graphs; (ii) Type-2 isomorphism, a new type of isomorphism other than already known Adam's isomorphism of circulant graphs and new abelian groups; (iii) Cartesian product and factorization of circulant graphs similar to the theory of product and factorization of natural numbers.
On factorisations of complete graphs into circulant graphs and the Oberwolfach Problem
Various results on factorisations of complete graphs into circulant graphs and on 2-factorisations of these circulant graphs are proved. As a consequence, a number of new results on the Oberwolfach Problem are obtained. For example, a complete solution to the Oberwolfach Problem is given for every 2-regular graph of order 2p where p = 5 (mod 8) is prime.
Isomorphism of circulant graphs and digraphs
Discrete Mathematics, 1979
Let Sc{l,...,n-1) satisfy -S =S mod n. The circulant graph G(n, S) with vertex set IQ, IJ l,"', u,_r} and edge set E satisfies "iiIj E E if and only if i -i E S, where all arithmetic is done mod n. The circulant digraph G(n, S) is defined similarly without the restriction S = -S. Adarn conjectured that G(n, S)=G(n, S') if and only if S = US' for some unit u mod n. In this paper we prove the conjecture true if n = pq where p and q are distinct primes. We also show that it is not generally true when n = p2, and determine exact conditions on S that it be tme in this case. We then show as a simple consequence that the conjecture is false in most cases when n is divisible by p2 where p is an odd prime, or n is divisible by 24.
On the cyclic decomposition of circulant graphs into almost
2011
It is known that if an almost bipartite graph G with n edges possesses a γlabeling, then the complete graph K 2nx+1 admits a cyclic G-decomposition. We introduce a variation of γ-labeling and show that whenever an almost bipartite graph G admits such a labeling, then there exists a cyclic Gdecomposition of a family of circulant graphs. We also determine which odd length cycles admit the variant labeling.
On the Ádám Conjecture on Circulant Graphs
Lecture Notes in Computer Science, 1998
We investigate the condition for isomorphism between circulant graphs which is known as theÁdám property. We describe a wide class of graphs for which theÁdám conjecture holds (and even in a stronger form refering to isospectrality rather than to isomorphism of graphs.
On the spectral Ádám property for circulant graphs
Discrete Mathematics, 2002
We investigate a certain condition for isomorphism between circulant graphs (known as the à Adà am property) in a stronger form by referring to isospectrality rather than to isomorphism of graphs. We describe a wide class of graphs for which the à Adà am conjecture holds. We apply these results to establish an asymptotic formula for the number of non-isomorphic circulant graphs and connected circulant graphs.
On the cyclic decomposition of circulant graphs into almost-bipartite graphs
Australas. J Comb., 2011
It is known that if an almost bipartite graph G with n edges possesses a γlabeling, then the complete graphK2nx+1 admits a cyclicG-decomposition. We introduce a variation of γ-labeling and show that whenever an almost bipartite graph G admits such a labeling, then there exists a cyclic Gdecomposition of a family of circulant graphs. We also determine which odd length cycles admit the variant labeling.