1. On the classification and dispersability of circulant graphs with two jump lengths.
- Author
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Yu, Xiaoxiang, Shao, Zeling, and Li, Zhiguo
- Subjects
- *
DIOPHANTINE equations , *BIPARTITE graphs , *CLASSIFICATION , *COMPLETE graphs - Abstract
In this paper, based on the Diophantine equation technique, we first prove the circulant graph C (Z n , { k 1 , k 2 }) is isomorphic to the disjoint union of gcd (n , k 1 , k 2) identical graphs, which belong to one of the three types of graphs: (i) C (Z n { 1 , k }) ; (i i) the Cartesian graph bundle C s □ φ C t over cycles; (i i i) the Cartesian product of the complete graph K 2 and a cycle. Naturally, to study the dispersability of C (Z n , { k 1 , k 2 }) can be reduced to study that of the above three types. Next, we solve the dispersability of the circulant graph C (Z n , { 1 , k }). Specifically, C (Z n , { 1 , k }) is dispersable if it is a bipartite; otherwise, it is nearly dispersable. In addition, we prove that bipartite circulant graphs are dispersable. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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