Combined Product of Two RL-graphs and It’s Applications

This paper introduces the notion of the combined product of two RL-graphs while it is an RL-graph. It is stated that the combined product has commutative properties, i.e., G ⊠ H and H ⊠ G are two isomorphic RL-graphs. Moreover, it is shown under a theorem that two isomorphic RL-graphs G and G ′ and two isomorphic RL-graphs H and H′ have isomorphic combined products G ⊠ H and G ′ ⊠ H′ . Further, it is investigated the relationships between these graphs and their operations by some notions such as strong RL-graph, regular RL-graph, and totally regular RL-graph. Afterward, it is displayed in a theorem that the combined product of two regular (α-regular, complete, connected) RL-graphs is a regular (α-regular, complete, connected) RL-graph. It is also shown in theorems what properties certain types of RL-graphs combined will have. Also, these notions and theorems are clarified by some examples. The combined product of two RL-graphs has many applications in various fields, such as probability sciences, urban planning, etc. In this article, only two of these applications, which determine the impact of effective factors on people’s quality of life and factors effective in raising the production of a factory, are stated and they are clarified by an example.