Abstract

For a graph $G$ of size $q$, an absolute mean graceful labeling $g$ of a graph $G$ is an injective mapping from the set of vertices of $G$ to the set $\{0,\pm 1,\pm 2,...,\pm q\}$ such that when each edge $vw$ is assigned the label $\bigl \lceil \frac{\lvert g(v)-g(w) \rvert}{2} \bigr \rceil$, the resulting edge labels are $1,2,...,q$. If a graph $G$ admits this labeling, then it is called an absolute mean graceful graph. In this paper, we construct some absolute mean graceful graphs of higher order obtained from cycles using various graph operations.

Keywords and Phrases

Absolute mean graceful labeling, Cycle, Cyclic snakes, Switching of a vertex, Duplication.

A.M.S. subject classification

05C78, 05C76, 05C38.

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