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Sum graphs over all the integers

✍ Scribed by Frank Harary

Publisher: Elsevier Science
Year: 1994
Tongue: English
Weight: 392 KB
Volume: 124
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(92)00054-u

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✦ Synopsis

We introduced the sum graph of a set S of positive integers as the graph G+(S) having S as its node set, with two nodes adjacent whenever their sum is in S. Now we study sum graphs over all the integers so that S may contain positive or negative integers on zero. A graph so obtained is called an integral sum graph. The sum number of a given graph G was defined as the smallest number of isolated nodes which when added to G result in a sum graph. The integral sum number of G is analogous. We see that all paths and all matchings are integral sum graphs. We find the integral sum number of the small graphs and offer several intriguing unsolved problems.

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