Journal of Mahani Mathematical Research

Journal of Mahani Mathematical Research

SH-graph automata with applications

Document Type : Research Paper

Authors
TianYu Zhang 1
Xiao Long Xin 2
Mohammad Mehdi Zahedi 3
1 School of Science, XI'an Polytechnic University, Shaanxi, China
2 Business School, Xi'an International University, Shaanxi, China
3 Department of Mathematics, Kerman Graduate University of Advanced Technology, Kerman, Iran
10.22103/jmmr.2026.26343.1905
Abstract
In this paper, because semihoops are the most basic residuated structure that contain all logical algebras based on Galois connections, therefore we introduce a new type fuzzy graph and its complement based on semihoops, denoted by $SH$-graph $G$ and $G^\prime$, respectively. Then, the $SH$-graph automata related to the $SH$-graph $G$ and a minimum zero forcing set are introduced, denoted by $A(Z(G))$. After that, the concepts of isomorphism between two $SH$-graphs $G_1$ and $G_2$ and isomorphism between two $SH$-graph automata $A(Z(G_1))$ and $A(Z(G_2))$ are introduced. Then, we prove that if two $SH$-graphs $G_1$ and $G_2$ are isomorphic, then two $SH$-graph automata $A(Z(G_1))$ and $A(Z(G_2))$ are isomorphic; otherwise it is not true. In addition, the concept of equivalence of $SH$-graph automata is proposed. Moreover, we prove that $SH$-graph automata obtained from the same $SH$-graphs are equivalent under different zero forcing sets in some special $SH$-graphs. And then, we know that $SH$-graph automata $A(Z(G_1))$ and $A(Z(G_2))$ are equivalent can not be characterized by $SH$-graphs $G_1$ and $G_2$ being isomorphic. Finally, we introduce a several of simple practical applications of $SH$-graph and $SH$-graph automata.
Keywords
semihoop
SH graph
SH-graph automata
isomorphism
equivalence
Subjects
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  • Receive Date 20 November 2025
  • Revise Date 30 January 2026
  • Accept Date 09 May 2026