Potential Subgraphs of the Missing Moore Graph

The possible existence of a Moore graph of diameter 2 and degree 57 has been an open question for more than six decades. In this paper, certain subgraphs of this graph, referred to as t-subgraphs, are considered. Exploiting symmetry by assuming a cyclic group of permutations representing edges joining leaf nodes of branches of a tree, a tractable constraint model for t-subgraphs is created. This can be solved using the Google OR Tools CP-SAT solver. Larger potential t-subgraphs than those currently known are constructed. This further extends a construction of certain sets of mutually orthogonal Latin rectangles. The implications for non-existence proofs of the Moore graph are considered.