On Kronecker Product Of Two RL-graphs And Some Related Results

Document Type : Research Paper

Authors

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

Abstract

Using the kronecker product definition of two simple graphs, the kronecker product of two RL-graphs was defined and is defined and it is further shown to be an RL-graph. Consequently, it is demonstrated that the kronecker product of two RL-graphs is commutative properties (i.e G⨂H = H⨂G). It is also stated that the kronecker product of two strong RL- graphs is a strong RL-graph but not necessarily vice-versa. It is bounded α and β of the kronecker product of two RL-graphs by α and β of its constituent graphs, respectively. Moreover, if H is an RL-graph, and G and G' are two isomorphic RL-graphs, then the kronecker product of G and H and the kronecker product of G' and H are isomorphic RLgraphs.
In addition, some notions such as regular RL-graphs, α-regular RL-graphs, and totally regular RL-graphs are proposed and explicated. One application of this operation, which has determined and estimated the group, having the maximum efficiency work among its members, is also suggested. Finally, it is brought one application of this operation that is  determined and estimated the group that has the maximum interact among its members. Ultimately, in light of the  above, some related theorems are proved and several examples are provided to illustrate these new notions.

Keywords

References

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Journal of Mahani Mathematical Research
Volume 11, Issue 3 - Serial Number 23
Special Issue dedicated to Prof. Mashaallah Mashinchi.
November 2022
Pages 87-107

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History

  • Receive Date: 03 May 2022
  • Revise Date: 13 June 2022
  • Accept Date: 04 July 2022

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