### Sufficient Conditions for the Connected $\beta$ - Deficient Graphs

#### Abstract

The deficiency of a graph $G$, denoted $def(G)$, is defined as the number of vertices which are not matched by a maximum matching in G. A graph $G$ is called $\beta$ - deficient if $def(G) \leq \beta$. In this note, we present sufficient condition for the connected $\beta$ - deficient graphs.

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