A bound on the dissociation number

The dissociation number diss ( G ) $\text{diss}(G)$ of a graph $G$ is the maximum order set vertices inducing subgraph that degree at most 1. Computing given algorithmically hard even when restricted to subcubic bipartite graphs. For with n $n$ vertices, m $m$ edges, k $k$ components, and c 1 ${c}_{1}$ induced cycles length modulo 3, we show ? ? 3 + $\text{diss}(G)\ge n-\frac{1}{3}(m+k+{c}_{1})$ . Furthermore, characterize extremal graphs in which every two are vertex-disjoint.