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math.CO2025
A Bipartite Graph Linking Units and Zero-Divisors
Shahram Mehry, Ali Eisapoor Khasadan
Let be a commutative ring with identity. We introduce a novel bipartite graph , the \textit{bipartite zero-divisor--unit graph}, whose vertex set is the disjoin…
math.CO2025
The Homomorphism Submodule Graph
Shahram Mehry, Mansour Molaeinejad
Let be a left -module. We define the \emph{homomorphism submodule graph} as the simple graph whose vertices are the proper submodules of , with an e…
math.CO2025
Directed Hamiltonicity in Generalized Kneser Graphs
Shahram Mehry
We prove that the canonical orientation of the generalized Kneser graph contains a directed Hamiltonian cycle for all integers and . Furthermore, we es…