Let $G$ be a simple connected graph. In this paper, Szeged dimension and PI$_v$ dimension of graph $G$ are introduced. It is proved that if $G$ is a graph of Szeged dimension $1$ then line graph of $G$ is 2-connected. The dimensions of five composite graphs: sum, corona, composition, disjunction and symmetric difference with strongly regular components is computed. Also explicit formulas of Sze...

In this paper, we present an effective method to characterize completely when a disconnected fractal square has only finitely many connected components. Our is establish some graph structures on squares reveal the evolution of connectedness during their geometric iterated construction. We also prove that every contains either or uncountably A few examples, including construction with exactly $m...