| Popis: |
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. |
