Geodesic
Maximum nontrivial convex cover number of join and corona of graphs
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 1 (2021), pp. 93-98 
Radu Buzatu. Maximum nontrivial convex cover number of join and corona of graphs. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 1 (2021), pp. 93-98. http://geodesic.mathdoc.fr/item/BASM_2021_1_a4/
@article{BASM_2021_1_a4,
     author = {Radu Buzatu},
     title = {Maximum nontrivial convex cover number of join and corona of graphs},
     journal = {Buletinul Academiei de \c{S}tiin\c{t}e a Republicii Moldova. Matematica},
     pages = {93--98},
     year = {2021},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BASM_2021_1_a4/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.

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