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MINIMUM RANK OF THE LINE GRAPH OF CORONA CnoKt

  • Im, Bokhee (Department of Mathematics Chonnam National University) ;
  • Lee, Hwa-Young (Department of Mathematics Chonnam National University)
  • Received : 2015.01.14
  • Published : 2015.04.30

Abstract

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.

Acknowledgement

Supported by : National Research Foundation of Korea(NRF)

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