On eigensharp and almost eigensharp graphs

Ghorbani E; Maimani HR

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On eigensharp and almost eigensharp graphs

机译：关于本征锐图和几乎本征锐图

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The minimum number of complete bipartite subgraphs needed to partition the edges of a graph G is denoted by b(G). A known lower bound on b(G) states that b(G) >= max{p(G), q(G)}, where p(G) and q(G) are the numbers of positive and negative eigenvalues of the adjacency matrix of G, respectively. When equality is attained, G is said to be eigensharp and when b(G) = max{p(G), q(G)} + 1. G is called an almost eigensharp graph. In this paper, we investigate the eigensharpness of graphs with at most one cycle and products of some families of graphs. Among the other results. we show that P-m V P-n, C-m V P-n for m equivalent to 2, 3 (mod 4) and Q(n) when n is odd are eigensharp. We obtain some results on almost eigensharp graphs as well.

机译：划分图G的边缘所需的完整二部图的最小数量由b（G）表示。 b（G）的已知下界表明b（G）> = max {p（G），q（G）}，其中p（G）和q（G）是正负本征值的数量G的邻接矩阵。当达到相等时，称G为本征锐度，当b（G）= max {p（G），q（G）} + 1时。G称为近本征锐图。在本文中，我们研究了最多具有一个周期的图的本征锐度以及一些图族的乘积。在其他结果中。我们证明，当n为奇数时，m等于2、3（模4）和Q（n）的P-m V P-n，C-m V P-n是本征锐化。我们也在几乎本征锐图上获得了一些结果。

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《Linear Algebra and its Applications》 |2008年第12期|共8页
作者
Ghorbani E; Maimani HR;
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正文语种 eng
中图分类线性代数;
关键词
Eigensharp graphs; Almost eigensharp graphs; Products of graphs;

机译：特征峰图;几乎特征峰图;图的乘积;

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机译：关于本征锐图和几乎本征锐图

On eigensharp and almost eigensharp graphs

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