Let the vertices of a graph 
be numbered with distinct integers 1 to 
. Then the dilation of 
is the maximum (absolute) difference between integers assigned
to adjacent vertices. Equivalently, it is the maximum value of 
over all nonzero elements of the adjacency
matrix 
.
Graph Dilation
See also
Graph BandwidthExplore with Wolfram|Alpha
References
West, D. B. Introduction to Graph Theory, 2nd ed. Englewood Cliffs, NJ: Prentice-Hall, p. 390, 2000.Cite this as:
Weisstein, Eric W. "Graph Dilation." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/GraphDilation.html