Title

Neighborhood degree lists of graphs

Document Type

Article

Date of Original Version

1-1-2018

Abstract

The neighborhood degree list (NDL) is a graph invariant that refines information given by the degree sequence and joint degree matrix of a graph and is useful in distinguishing graphs having the same degree sequence. We show that the space of realizations of an NDL is connected via a switching operation. We then determine the NDLs that have a unique realization by a labeled graph; the characterization ties these NDLs and their realizations to the threshold graphs and difference graphs.

Publication Title

Discrete Mathematics

Volume

341

Issue

1

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