• KUKIL KALPA RAJKHOWA

      Articles written in Proceedings – Mathematical Sciences

    • Non-comaximal graph of ideals of a ring

      BIKASH BARMAN KUKIL KALPA RAJKHOWA

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      Let R be a ring. The non-comaximal graph of R, denoted by $NC(R)$ is an undirected graph whose vertex set is the collection of all non-trivial (left) ideals of $R$ and any two distinct vertices $I$ and $J$ are adjacent if and only if $I + J \neq R$. The concepts of connectedness, independent set, clique and traversability of $NC(R)$ are discussed.

    • Prime intersection graph of ideals of a ring

      KUKIL KALPA RAJKHOWA HELEN K SAIKIA

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      Let $R$ be a ring. The prime intersection graph of ideals of $R$, denoted by $G_{P}(R)$, is the graph whose vertex set is the collection of all non-trivial (left) ideals of $R$ with two distinct vertices $I$ and $J$ are adjacent if and only if $I \cap J \neq 0$ and either one of $I$ or $J$ is a prime ideal of $R$. We discuss connectedness in $G_{P}(R)$. The concepts of bipartition, planarity and colorability are interpreted. Finally, we introduce the idea of traversability in $G_{P}(\mathbb{Z}_{n})$. The core part of this paper is observed in the ring $\mathbb{Z}_{n}$.

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