GRAPHS WITH ISOMORPHIC NEIGHBOR-SUBGRAPHS

Abstract

A graph G is said to be H-regular if for each vertex v is an element of V(G), the graph induced by N(G)(v) is isomorphic to H. A graph H is a feasible neighbor-subgraph if there exists an H-regular graph, otherwise H is a forbidden neighbor-subgraph. In this paper, we obtain some classes of graphs H which are forbidden and then we focus on searching H-regular graphs especially those graphs of smaller order.