Bapat, R. B. ; Lal, A. K.
(1991)
*Path-positive graphs*
Linear Algebra and its Applications, 149
.
pp. 125-149.
ISSN 0024-3795

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Official URL: http://www.sciencedirect.com/science/article/pii/0...

Related URL: http://dx.doi.org/10.1016/0024-3795(91)90330-Y

## Abstract

For any positive integer k let P_{k} denote the characteristic polynomial of the adjacency matrix of the path on k vertices. We obtain certain results regarding P_{k} evaluated at A(G), the adjacency matrix of any given graph G. For some special graphs G, we describe the matrix P_{k}(A(G)) completely. We call a graph G path-positive if P_{k}(A(G)) is a nonnegative matrix for all positive integers k. It is shown that if G is a connected graph with a vertex of degree at least four, then G is path-positive. We conjecture that all connected graphs are path-positive apart from a few exceptional cases described in the paper.

Item Type: | Article |
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Source: | Copyright of this article belongs to Elsevier Science. |

ID Code: | 78315 |

Deposited On: | 19 Jan 2012 06:31 |

Last Modified: | 19 Jan 2012 06:31 |

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