Communications of the
Korean Mathematical Society CKMS

The minimum rank $\mr(G)$ of a simple graph $G$ is defined to be the smallest possible rank over all symmetric real matrices whose $(i,j)$-th entry (for $i\neq j$) is nonzero whenever $\{i,j\}$ is an edge in $G$ and is zero otherwise. The corona $C_n\circ K_t$ is obtained by joining all the vertices of the complete graph $K_t$ to each $n$ vertex of the cycle $C_n$. For any $t$, we obtain an upper bound of zero forcing number of $L(C_n\circ K_t)$, the line graph of $C_n\circ K_t$, and get some bounds of $\mr(L(C_n\circ K_t))$. Specially for $t=1,2$, we have calculated $\mr(L(C_n\circ K_t))$ by the cut-vertex reduction method.

Keywords: minimum rank, zero forcing, line graph, corona, ciclo

MSC numbers: Primary 05C50; Secondary 15A03