Abstract
If D = ( V, A) is an acyclic diagraph and G = ( V, E) is a graph such that two vertices x and y are adjacent in G if and only if they have a common predator vertex or prey vertex in D, then G is called a niche graph. It is easy to show that not all graphs are niche graphs. However in many cases it is possible to adjoin a finite set of vertices, say I m , to the vertex set V of both G and D, and also some additional arcs to the arc set to obtain G′ and D′ respectively where G′ is a niche graph, V′ = V∪ I m and E′ = E. The smallest number of vertices that one must adjoin to G to obtain a niche graph is called the niche number of G. Some classes of niche graphs are investigated, including paths and cycles. We also calculate the niche number of some other graphs. An infinite class of graphs is exhibited in which none of the graphs in that class has a niche number and a characterization of niche graphs is given.
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