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The Path polynomials Evaluated at Some Matrices(PDF)


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The Path polynomials Evaluated at Some Matrices
Shi Ronghua Zheng Shoubing ①
School of Adult Education, NUST, Nanjing 210094)
mat rix es ( mathemat ics ) characterist ic polynomial connected graph t rees ( mathemat ics)
For any po sit ive integer k ≥ 1, the paper denoted by Pk ( K) the char acteristic polynomial of the t ridiag onal matr ix w ith 1ps on the super -and subdiago nals and zeres elsew here. The n×n square mat rix A is said to be path-posit iv e if Pk ( A ) ≥ 0 for k= 1, 2, 3, ? A graph is said to path-po sit iv e if and only if the adjacency matrix of the g raph is path-posit ive. This paper has derived the str ucture formulas of path-po lynomials evaluated at the adjacency matr ices of gr aphs D , E and F , respect iv ely . T his w ork serves as the basis for further invest ig at ing the behavior of P k( A ) ev aluated at arbit rary unreduced ( 0, 1) symmet ric mat rices.


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Last Update: 2013-04-11