7 research outputs found
On Jacobian group of the -graph
In the present paper we compute the Jacobian group of -graph
The notion of -graph continues the list of
families of -, - and -graphs well-known in the graph theory. In
particular, graph is isomorphic to discrete torus
It this case, the structure of the Jacobian group will be find
explicitly.Comment: arXiv admin note: text overlap with arXiv:2111.0430
The number and degree distribution of spanning trees in the Tower of Hanoi graph
The number of spanning trees of a graph is an important invariant related to topological and dynamic properties of the graph, such as its reliability, communication aspects, synchronization, and so on. However, the practical enumeration of spanning trees and the study of their properties remain a challenge, particularly for large networks. In this paper, we study the number and degree distribution of the spanning trees in the Hanoi graph. We first establish recursion relations between the number of spanning trees and other spanning subgraphs of the Hanoi graph, from which we find an exact analytical expression for the number of spanning trees of the n-disc Hanoi graph. This result allows the calculation of the spanning tree entropy which is then compared with those for other graphs with the same average degree. Then, we introduce a vertex labeling which allows to find, for each vertex of the graph, its degree distribution among all possible spanning trees.Postprint (author's final draft