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.
Recommended Citation
Baumer, Benjamin; Wei, Yijin; and Bloom, Gary S., "The Smallest Non-Autograph" (2016). Mathematics and Statistics: Faculty Publications, Smith College, Northampton, MA.
https://scholarworks.smith.edu/mth_facpubs/18
Comments
Archived as published.