Abstract
The edge-induced subgraph on the set of all edges of a graph G that are adjacent to a given vertex x is called the neighbourhood of the second type of x in G and is denoted by N 2( x, G) (an edge yz is said to be adjacent to x if y≠ x≠ z and y or z is adjacent to x). A graph G is N 2-locally disconnected if N 2( x, G) is disconnected for every vertex x of G. The main aim of the present paper is to find the maximum size of an N 2-locally disconnected graph of a given order.
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