m-Bonacci graceful labeling

Abstract

We introduce new labeling called m-bonacci graceful labeling. A graph G on n edges is m-bonacci graceful if the vertices can be labeled with distinct integers from the set $\{0,1,2,\dots ,Z_{n,m}\}$ such that the derived edge labels are the first n m-bonacci numbers. We show that complete graphs, complete bipartite graphs, gear graphs, triangular grid graphs, and wheel graphs are not m-bonacci graceful. Almost all trees are m-bonacci graceful. We give m-bonacci graceful labeling to cycles, friendship graphs, polygonal snake graphs, and double polygonal snake graphs.

Keywords:

• m-Bonacci number
• graceful graph

Additional information

Funding

The second author wishes to acknowledge the fellowship received from Department of Science and Technology under INSPIRE fellowship (IF170077).