Advances and Applications in Discrete Mathematics
Volume 17, Issue 2, Pages 169 - 184
(April 2016) http://dx.doi.org/10.17654/AADMApr2016_169_184 |
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ON THE PATH MATRICES OF GRAPHS AND THEIR PROPERTIES
S. C. Patekar and M. M. Shikare
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Abstract: Let G be a graph with vertex set We define a matrix whose th entry is the maximum number of vertex disjoint paths between the corresponding vertices if they are adjacent and zero otherwise. We call this matrix as path matrix of G and its eigenvalues as path eigenvalues of G. In this paper, we investigate path eigenvalues of some specific classes of graphs. The nature of largest path eigenvalues and relation between chromatic number and largest path eigenvalue have been explored. |
Keywords and phrases: path, spanning subgraphs, real symmetric matrix, eigenvalues, line graph. |
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