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A set of vertices is called a ▫$k$▫-limited dominating set if every vertex of the graph is either contained in the set or adjacent to a vertex of the set, and each vertex of the set has at most ▫$k$▫ neighbors outside the set. The minimum cardinality among all ▫$k$▫-limited dominating sets of ▫$G$▫ ...

The $\sigma$-irregularity index is a variant of the well-established Albertson irregularity index. For a graph $G = (V, E)$ it is defined as $\sigma (G) = \Sigma _{uv\in E}(d(u) − d(v))^2$, where $d(u)$ and $d(v)$ denote the degrees of vertices $u$ and $v$, respectively. In this note, we characteriz ...

The ▫$\sigma$▫-irregularity, a variant of the well-established Albertson irregularity, is a topological invariant defined for a graph ▫$G=(V,E)$▫ as ▫$\sigma (G) = \sum_{u,v \in E}(d(u) - d(v))^2$▫, where ▫$d(u)$▫ and ▫$d(v)$▫ denote the degrees of vertices ▫$u$▫ and ▫$v$▫, respectively. Recent rese ...