Year: 2026
Type: article
Abstract: 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, traversability and planarity of $\varepsilon(G)$. The concept of a divisor subgroup with respect to a subgroup of $G$ is introduced, whose effect is observed in some of the characterizations of $\varepsilon(G)$.
Institutions: Gauhati University, Cotton University
Language: English
Topic: Finite Group Theory Research
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W7210285035