Some Properties of L-graphs

This paper introduces a graph built on a residual lattice called the L graph. It determines the notion of the strong L-graph. It introduces new concepts, such as direct sum and direct product of two L-graphs. The L-graphs have many applications. For instance, they help determine the minimum number of hospitals equipped with all the treatment wards needed. Accordingly, some related theorems have been proven and several examples have been provided to illustrate these new concepts.