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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 andgirth g. This catalog is compared with other known lists of (3, g) graphs suchas the enumerations of trivalent symmetric graphs and enumerations of trivalentvertex-transitive graphs, to conclude that this catalog has graphs for moreorders than these lists. This catalag also specifies a list of orders,rotational symmetry and girth for which the class of (3, g) graphs do notexist. It is also shown that this catalog of graphs extends infinitely.

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