Document Type

Article

Publication Date

2016

Publication Title

Discussiones Mathematicae Graph Theory

Abstract

Suppose that G is a simple, vertex-labeled graph and that S is a multiset. Then if there exists a one-to-one mapping between the elements of S and the vertices of G, such that edges in G exist if and only if the absolute difference of the corresponding vertex labels exist in S, then G is an autograph, and S is a signature for G. While it is known that many common families of graphs are autographs, and that infinitely many graphs are not autographs, a non-autograph has never been exhibited. In this paper, we identify the smallest non-autograph: a graph with 6 vertices and 11 edges. Furthermore, we demonstrate that the infinite family of graphs on n vertices consisting of the complement of two non-intersecting cycles contains only non-autographs for n≥8.

Keywords

graph labeling, difference graphs, autographs, monographs

Volume

36

First Page

577

Last Page

602

DOI

doi:10.7151/dmgt.1881

Rights

Licensed to Smith College and distributed CC-BY under the Smith College Faculty Open Access Policy.

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