For an R-module M and f ∈ M∗ = Hom(M, R), let Zf(M) and Regf(M) be the sets of all zero-divisors elements and regular elements of M with re- spect to f, respectively. In this paper, we introduce the total graph of M with respect to f, denoted by T(Γf(M)), which is the graph with all the elements M as vertices, and for distinct elements m, n ∈ M, m and n are adjacent and only if m + n ∈ Zf(M). We also study the subgraphs Z(Γf(M)) and Reg(Γf(M)) with vertices Zf(M) and Regf(M), respectively.
Baziar, M. and Zare Khafri, S. (2024). Some properties of the graph of modules with respect to a first dual homomorphism. Journal of Advanced Mathematical Modeling, 14(3-English), 121-129. doi: 10.22055/jamm.2025.47571.2298
MLA
Baziar, M. , and Zare Khafri, S. . "Some properties of the graph of modules with respect to a first dual homomorphism", Journal of Advanced Mathematical Modeling, 14, 3-English, 2024, 121-129. doi: 10.22055/jamm.2025.47571.2298
HARVARD
Baziar, M., Zare Khafri, S. (2024). 'Some properties of the graph of modules with respect to a first dual homomorphism', Journal of Advanced Mathematical Modeling, 14(3-English), pp. 121-129. doi: 10.22055/jamm.2025.47571.2298
CHICAGO
M. Baziar and S. Zare Khafri, "Some properties of the graph of modules with respect to a first dual homomorphism," Journal of Advanced Mathematical Modeling, 14 3-English (2024): 121-129, doi: 10.22055/jamm.2025.47571.2298
VANCOUVER
Baziar, M., Zare Khafri, S. Some properties of the graph of modules with respect to a first dual homomorphism. Journal of Advanced Mathematical Modeling, 2024; 14(3-English): 121-129. doi: 10.22055/jamm.2025.47571.2298
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