Edge Imbalance Sequences And Their Graphicness

The imbalance of a given edge in a graph is the absolute difference between the degrees of its vertices. The multiset of all edge imbalances in G is called its imbalance sequence and denoted by M_{G}. In this paper, we focus on unary and binary graph operations that preserve the graphicness of imbalance sequences. For example, we prove that if a graph G' is obtained from G by "replacing" each vertex with a complete graph of sufficiently large order, then the graphicness of M_{G} implies the graphicness of M_{G'}. Also, we discuss several conjectures related to the graphicness of the imbalance sequence of a graph and explore connections between them.