Alpha Adjacency: A generalization of adjacency matrices
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B. Shader and W. So introduced the idea of the skew adjacency matrix. Their idea was to give an orientation to a simple undirected graph G from which a skew adjacency matrix S(G) is created. The -adjacency matrix extends this idea to an arbitrary field F. To study the underlying undirected graph, the average -characteristic polynomial can be created by averaging the characteristic polynomials over all the possible orientations. In particular, a Harary-Sachs theorem for the average-characteristic polynomial is derived and used to determine a few features of the graph from the average-characteristic polynomial.
2017 ◽
Vol 16
(06)
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pp. 1750120
1992 ◽
Vol 1
(1)
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pp. 13-25
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1980 ◽
Vol 2
(4)
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pp. 349-351
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