A Theorem on k -Saturated Graphs

Source abstract

In this paper we consider finite graphs without loops and multiple edges. A graph is considered to be an ordered pair 〈G, *〉 where G is a finite set the elements of which are called the vertices of while * is a subset of [ G ] 2 (where [ G ] 2 is the set of all subsets of two elements of G ). The elements of * are called the edges of . If { P , Q } ∊ *, we say that Q is adjacent to P . The degree of a vertex is the number of vertices adjacent to it. Let k be an integer. We say that is the complete k - graph if G has k elements and * = [ G ] 2 .