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Generalized Sum Graphs Department of Mathematics

Summary: Generalized Sum Graphs
Noga Alon
Department of Mathematics
Raymond and Beverly Sackler Faculty of Exact Sciences
Tel Aviv University
Ramat Aviv , Tel Aviv 69978 Israel
Edward R. Scheinerman
Department of Mathematical Sciences
The Johns Hopkins University
Baltimore, Maryland 21218 USA
Harary [8] calls a finite, simple graph G a sum graph if one
can assign to each vi V (G) a label xi so that {vi, vj} E(G) iff
xi + xj = xk for some k. We generalize this notion by replacing
"xi + xj" with an arbitrary symmetric polynomial f(xi, xj). We
show that for each f, not all graphs are "f-graphs". Furthermore,
we prove that for every f and every graph G we can transform G
into an f-graph via the addition of |E(G)| isolated vertices. This
result is nearly best possible in the sense that for all f and for
all m 1


Source: Alon, Noga - School of Mathematical Sciences, Tel Aviv University


Collections: Mathematics