Open Support of Hypergraphs under Addition

Abstract

For a vertex v in a graph G, the open support of v under addition is the sum of degrees of all its neighbors. The open support of G under addition is the sum of open supports of all its vertices. The results for open support of graphs are deeply dependent on the structure property of the graph considered, such as its symmetry. In this paper, we generalize the concept of open support to hypergraphs. We give some examples and prove a general formula for open support of hypergraphs by using the adjacency and incidence matrices method.