Some properties of catalog of (3, g) Hamiltonian bipartite graphs: orders, non-existence and infiniteness

Abstract

The focus of this paper is on discussion of a catalog of a class of (3, g) graphs for even girth g. A (k, g) graph is a graph with regular degree k and girth g. This catalog is compared with other known lists of (3, g) graphs such as the enumerations of trivalent symmetric graphs and enumerations of trivalent vertex-transitive graphs, to conclude that this catalog has graphs for more orders than these lists. This catalag also specifies a list of orders, rotational symmetry and girth for which the class of (3, g) graphs do not exist. It is also shown that this catalog of graphs extends infinitely.

arXiv comment21 pages. arXiv admin note: text overlap with arXiv:1201.5317 by other authors