Document Type : Research Paper

**Authors**

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

**Abstract**

The current study aimed to describe the notion of the L-graph, which is constructed on a residuated lattice, presenting the idea of the maximal product of two L-graphs.

Moreover, the applied algorithm demonstrated its efficiency to a great extent to improve the educational system.

The results showed that the maximal product of both G and H and reversely, H

and G are isomorphic L-graphs.

The maximal product of two L-graph automata was represented as a new notion,

followed by investigating their self-sufficiency conditions in two different modes.

In addition, A(Z(G))\star~A(Z(H)) and A(Z(H))\star~A(Z(G)) were proved as two isomorphic-related L-graph automata considering the residuated lattice properties.

Then, correlations among A(Z(G))\star A(Z(H)), A(Z(G)), and A(Z(H)) behaviors were explained.

As a result, some theorems of the relationship between L-graph automata and their maximal product were introduced.

Subsequently, some related theorems were proved, and several examples were provided to illustrate these new notions. Further, an application of the maximal product of two related L-graph automata was expressed in the factors affecting the spared of the coronavirus, and accordingly,

some solutions were suggested to reduce the spread of the virus.

Moreover, the applied algorithm demonstrated its efficiency to a great extent to improve the educational system.

The results showed that the maximal product of both G and H and reversely, H

and G are isomorphic L-graphs.

The maximal product of two L-graph automata was represented as a new notion,

followed by investigating their self-sufficiency conditions in two different modes.

In addition, A(Z(G))\star~A(Z(H)) and A(Z(H))\star~A(Z(G)) were proved as two isomorphic-related L-graph automata considering the residuated lattice properties.

Then, correlations among A(Z(G))\star A(Z(H)), A(Z(G)), and A(Z(H)) behaviors were explained.

As a result, some theorems of the relationship between L-graph automata and their maximal product were introduced.

Subsequently, some related theorems were proved, and several examples were provided to illustrate these new notions. Further, an application of the maximal product of two related L-graph automata was expressed in the factors affecting the spared of the coronavirus, and accordingly,

some solutions were suggested to reduce the spread of the virus.

**Keywords**

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May and June 2022

Pages 107-126