The Common-Neighbourhood of a Graph
نویسندگان
چکیده
Abstract: The most widely used and well-known vulnerability measures of a connected graph are based on the neighbourhood concept. It takes into account neighbour-integrity, edge-integrity and accessibility number. In this work we define and examine common-neighbourhood of a connected graph as a new global connectivity measure. Our measure examines the neighbourhoods of all pairs of vertices of any connected graph. We show that, for connected graphs G1 and G2 of the same order, if the dominating number of G1 is bigger than the dominating number of G2, then the common-neighbourhood of G1 is less than the common-neighbourhood of G2. We give some theorems and obtain some results on common-neighbourhood of a graph. We consider all the graphs in this paper as connected, undirected and without loops.
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