On real number labelings and graph invertibility

Real Number Labelings for Paths and Cycles Real Number Labelings for Paths and Cycles *

The problem of radio channel assignments with multiple levels of interference depending on distance can be modeled using graph theory. The authors previously introduced a model of labeling by real numbers. Given a graph G, possibly infinite, and real numbers k1, k2, . . . , kp ≥ 0, a L(k1, k2, . . . , kp)-labeling of G assigns real numbers f(x) ≥ 0 to the vertices x, such that the labels of ver...

Real Number Labelings for Paths and Cycles

The problem of radio channel assignments with multiple levels of interference depending on distance can be modeled using graph theory. The authors previously introduced a model of labeling by real numbers. Given a graph G, possibly infinite, and real numbers k1, k2, . . . , kp ≥ 0, a L(k1, k2, . . . , kp)-labeling of G assigns real numbers f(x) ≥ 0 to the vertices x, such that the labels of ver...

Optimal Real Number Graph Labelings of a Subfamily of Kneser Graphs

A notion of real number graph labelings captures the dependence of the span of an optimal channel assignment on the separations that are required between frequencies assigned to close transmitters. We determine the spans of such optimal labelings for a subfamily of Kneser graphs formed by the complements of the line graphs of complete graphs. This subfamily contains (among others) the Petersen ...

Some Open Problems on Graph Labelings

In this note we present some of the open problems on various aspects of graph labelings which were posed by the participants during IWOGL 2009 and which have not been included in any of the other papers appearing in this volume.

Further results on antimagic graph labelings