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 Bandwidth## Explore 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