Graphs derivable from L₃(5) graphs

Abstract

We show that corresponding to a latin square of order 5 with an orthogonal mate there is essentially a unique L₃(5) graph G₁. Similarly corresponding to a latin square of order 5 without an orthogonal mate there is a unique L₃(5) graph G₂. G₁ is the only member in the weak-equivalence class containing it and G₁ has a unique pseudo-(3, 6, 3) graph as an ascendant. The weak-equivalence class containing G₂ contains precisely the complement of G₂ and two other graphs which are complements of each other. G₂ has exactly two nonisomorphic pseudo-(3, 6, 3) graphs as ascendants. Both the weak-equivalence classes are closed with respect to complementation and hence the other possible ascendants of G₁ and G₂ respectively are nothing but the complements of the corresponding pseudo-(3, 6, 3) ascendants mentioned above.