Super Connectivity and Super Edge-connectivity of Transformation Graphs \(G^{+-+}\)

Abstract

For a graph \(G = (V(G), E(G))\), the transformation graph \(G^{+-+}\) is the graph with vertex set \(V(G) \cup E(G)\) in which the vertices \(\alpha\) and \(\beta\) are joined by an edge if and only if \(\alpha\) and \(\beta\) are adjacent or incident in \(G\) while \(\{\alpha, \beta\} \not\subseteq E(G)\), or \(\alpha\) and \(\beta\) are not adjacent in \(G\) while \(\{\alpha, \beta\} \in E(G)\). In this note, we show that all but for a few exceptions, \(G^{+-+}\) is super-connected and super edge-connected.