Abstract

A degree associated edge card of a graph G is an edge deleted subgraph of G with which the degree of the deleted edge is given. The degree associated edge reconstruction number of a graph G (or dern(G)) is the size of the smallest collection of the degree associated edge cards of G that uniquely determines G. A split graph G is a graph in which the vertices can be partitioned into an independent set and a clique. We prove that the dern of all split graphs with biregular independent set is one.

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