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MINIMUM RANK OF THE LINE GRAPH OF CORONA CnoKt
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 Title & Authors
MINIMUM RANK OF THE LINE GRAPH OF CORONA CnoKt
Im, Bokhee; Lee, Hwa-Young;
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 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 ) is nonzero whenever {i, j} is an edge in G and is zero otherwise. The corona is obtained by joining all the vertices of the complete graph to each n vertex of the cycle . For any t, we obtain an upper bound of zero forcing number of , the line graph of , and get some bounds of . Specially for t = 1, 2, we have calculated by the cut-vertex reduction method.
 Keywords
minimum rank;zero forcing;line graph;corona;ciclo;
 Language
English
 Cited by
 References
1.
AIM Minimum Rank-Special Graphs Work Group(1-AIM), Zero forcing sets and the minimum rank of graphs, Linear Algebra Appl. 428 (2008), no. 7, 1628-1648. crossref(new window)

2.
E. Almodovar, L. DeLoss, L. Hogben, K. Hogenson, K. Murphy, T. Peters, and C. A. Ramrez, Minimum rank, maximum nullity and zero forcing number for selected graph families, Involve 3 (2010), no. 4, 371-392. crossref(new window)

3.
F. Barioli, S. M. Fallat, and L. Hogben, Computation of minimal rank and path cover number for certain graphs, Linear Algebra Appl. 392 (2004), 289-303. crossref(new window)

4.
S. M. Fallat and L. Hogben, The minimum rank of symmetric matrices described by a graph: a survey, Linear Algebra Appl. 426 (2007), no. 2-3, 558-582. crossref(new window)

5.
L. Y. Hsieh, On minimum rank matrices having prescribed graph, Ph.D. Thesis, University of Wisconsin-Madison, 2001.

6.
P. M. Nylen, Minimum-rank matrices with prescribed graph, Linear Algebra Appl. 248 (1996), 303-316. crossref(new window)