Abstract:
Let $G$ be a connected graph. We say that a set $S\subseteq X(G)$ is convex in $G$ if, for any two vertices $x,y\in S$, all vertices of every shortest path between $x$ and $y$ are in $S$. If $3\leq|S|\leq|X(G)|-1$, then $S$ is a nontrivial set. The greatest $p\geq2$ for which there is a cover of $G$ by $p$ nontrivial and convex sets is the maximum nontrivial convex cover number of $G$. In this paper, we determine the maximum nontrivial convex cover number of join and corona of graphs.
Keywords and phrases:convex cover, join of graphs, corona of graphs.
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