Minimum rank, maximum nullity and zero forcing number for selected graph families

Autor:	Kaitlyn Murphy, Leslie Hogben, Travis Peters, Edgard Almodovar, Camila A. Ramírez, Laura DeLoss, Kirsten Hogenson
Rok vydání:	2010
Předmět:	Discrete mathematics 15A18 Simple graph dual ciclo General Mathematics estrella 15A03 Graph Combinatorics 2 × 2 real matrices minimum rank Zero Forcing Equalizer 05C50 zero forcing number maximum nullity Mathematics
Zdroj:	Involve 3, no. 4 (2010), 371-392
ISSN:	1944-4184 1944-4176
DOI:	10.2140/involve.2010.3.371
Popis:	The minimum rank of a simple graph [math] is defined to be the smallest possible rank over all symmetric real matrices whose [math] -th entry (for [math] ) is nonzero whenever [math] is an edge in [math] and is zero otherwise. Maximum nullity is taken over the same set of matrices, and the sum of maximum nullity and minimum rank is the order of the graph. The zero forcing number is the minimum size of a zero forcing set of vertices and bounds the maximum nullity from above. This paper defines the graph families ciclos and estrellas and establishes the minimum rank and zero forcing number of several of these families. In particular, these families provide examples showing that the maximum nullity of a graph and its dual may differ, and similarly for the zero forcing number.
Databáze:	OpenAIRE
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