N. Hazarika

Essential graph of an abelian group

The essential graph of an abelian group $G$, denoted by $\varepsilon(G)$, is an undirected graph with vertex set as the collection of all non-trivial proper subgroups of $G$ and any two distinct vertices $A$ and $B$ are adjacent if and only if $AB$ is an essential subgroup of $G$. We discuss connectedness, traversabili...