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\boxtimes H‎ ‎and‎ ‎H\boxtimes 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\boxtimes H‎ ‎and‎ ‎G'\boxtimes 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 (\alpha-regular‎, ‎complete‎, ‎connected) RL-graphs is a regular (\alpha-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.

Keywords:

RL-graph‎ , ‎Regular RL-graph‎ , ‎Combined product of two RL-graphs‎