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Sequential Graph


A connected graph having e graph edges is said to be sequential if it is possible to label the nodes i with distinct integers f_i in {0,1,2,...,e-1} such that when graph edge ij is labeled f_i+f_j, the set of graph edge labels is a block of e consecutive integers (Grace 1983, Gallian 1990). No harmonious graph is known which cannot also be labeled sequentially.


See also

Connected Graph, Harmonious Graph

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References

Gallian, J. A. "Open Problems in Grid Labeling." Amer. Math. Monthly 97, 133-135, 1990.Grace, T. "On Sequential Labelings of Graphs." J. Graph Th. 7, 195-201, 1983.

Referenced on Wolfram|Alpha

Sequential Graph

Cite this as:

Weisstein, Eric W. "Sequential Graph." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SequentialGraph.html

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