Let ϛ be a commutative semiring with identity. The non-comaximal graph ᴏf ϛ indicated by ɣ(ϛ) an undirected graph where ϛ is the ᵴet ᴏf vertices in ɣ(ϛ) and d,e∈ϛ are adjacent if and ᴏnly if ϛd+ϛe≠ϛ. The concepts of connectedness, independent set, clique besides girth of ɣ(ϛ) are discussed.
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Tuama et al. (2025) studied this question.