A connected graph having 
graph edges is said to be sequential
if it is possible to label the nodes 
with distinct integers 
in 
such that when graph
edge 
is labeled 
,
the set of graph edge labels is a block of 
consecutive integers (Grace 1983, Gallian 1990). No harmonious
graph is known which cannot also be labeled sequentially.
Sequential Graph
See also
Connected Graph, Harmonious GraphExplore with Wolfram|Alpha
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 GraphCite this as:
Weisstein, Eric W. "Sequential Graph." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SequentialGraph.html