A Connected Graph having Edges is said to be sequential if it is possible to label the nodes with distinct Integers in such that when Edge is labeled , the set of Edge labels is a block of consecutive integers (Grace 1983, Gallian 1990). No Harmonious Graph is known which cannot also be labeled sequentially.
See also Connected Graph, Harmonious Graph
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.