Some applications of maximal product in RL-graphs

Document Type : Original Article


Department of Mathematics, Kerman Graduate University of Advanced Technology, Kerman, Iran


This research targets the investigation of characteristics within the maximal product of two RL-graphs by scrutinizing  particular types of RL-graphs. Our first step in this quest entails introducing RL-graph concepts, followed by defining  what constitutes a strong RL-graph, further elucidated by a practical example. Subsequently, we lay out the connection  between RL-graphs and their maximal products. In particular, a theorem establishes that two RL-graphs are regular if  their maximal product maintains regularity, and a parallel rule applies to α-regular RL-graphs. Contrarily, the reverse is  not inherently true, a claim supported by a specific example. Nonetheless, by incorporating an additional condition, we  validate the converse. Lastly, we assert that two RL-graphs are connected only if their maximal product is also a  connected RL-graph. In conclusion, the maximal product of two RL-graphs holds potential in modeling societal health  metrics and road accident rates. 


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