On the connectivity of k-distance graphs

Abstract

For any k ∈ N, the k−distance graph D k G has the same vertex set of G, and two vertices of D k G are adjacent if they are exactly distance k apart in the original graph G. In this paper, we consider the connectivity of D k G and state the conditions for graph G and integer k such that the graph D k G is connected.

On n-connected minors of the es-splitting binary matroids

“…x k y h y 2 y 1 e q q q q q q r r r r r x k v y 1 y 2 y h a e γ q q q q q q G H splitting operation along with some other operations. The notion of connectivity of graphs also has been studied in [6,13] and connectivity of binary matroids has been studied in [3,14]. Suppose G is a graph with n vertices and m edges.…”