Abstract

A graph $G$ with $q$ edges is said to be absolute mean graceful if there is a one-to-one function $f$ from $V(G)$ to the set $\{0,\pm 1,\pm 2, \pm 3,\hdots,\pm q\}$ such that when each edge $xy$ is assigned the label $\bigl \lceil \frac{\lvert f(x)-f(y) \rvert}{2} \bigr \rceil$, then the resulting edge labels are distinct. In this paper, the absolute mean graceful labeling of $m$-splitting and degree splitting graphs of some graphs are investigated.

Keywords and Phrases

Absolute mean graceful labeling, m-splitting graph, splitting graph, degree splitting graph.

A.M.S. subject classification

05C78, 05C76.

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