Geodesic
On the inclusion submodule graph of a module
Novi Sad Journal of Mathematics, Tome 52 (2022) no. 1.

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Let $R$ be a ring with identity and $M$ be a unitary left $R$-module. The inclusion submodule graph of a module $M$, denoted by $In(M)$, is an undirected simple graph whose vertex set $V(In(M))$ is a set of all nontrivial submodules of $M$ and there is an edge between two distinct vertices $X$ and $Y$ if and only if $ X\subset Y$ or $ Y\subset X$. In this paper, we investigate connections between the graph-theoretic properties of $In(M)$ and some algebraic properties of modules. In particular, we consider several properties of the graph $In(M)$, such as connectivity, diameter and girth. Also we obtain some independent sets and universal vertices of this graph. We characterize some modules for which the inclusion submodule graphs are connected, complete and null. Finally, we study the clique number and the chromatic number of $In(M)$.
Publié le :
DOI : 10.30755/NSJOM.10828
Classification : 05C15, 05C25, 05C69, 16D10
Keywords: inclusion submodule graph, diameter, girth, clique number, chromatic number 
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     title = {On the inclusion submodule graph of a module},
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     year = {2022},
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Lotf Ali Mahdavi; Yahya Talebi. On the inclusion submodule graph of a module. Novi Sad Journal of Mathematics, Tome 52 (2022) no. 1. doi : 10.30755/NSJOM.10828. http://geodesic.mathdoc.fr/articles/10.30755/NSJOM.10828/

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