Weighted Adjacency Matrix of a Semigraph and its Spectral Analysis
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In this paper we introduce weighted adjacency matrix W(G) of a semigraph G and study the related spectral properties similar to the spectral properties of the adjacency matrix of graphs. We prove Sachs type theorem by interpreting first few coefficients of the characteristic polynomial of W(G) in terms of the semigraph parameters. We extend Harary formula for the determinant of the adjacency matrix of graphs to the weighted adjacency matrix of semigraphs. We find bounds for eigenvalues and energy for certain classes of semigraphs.
Abstract
In this paper we introduce weighted adjacency matrix W(G) of a semigraph G and study the related spectral properties similar to the spectral properties of the adjacency matrix of graphs. We prove Sachs type theorem by interpreting first few coefficients of the characteristic polynomial of W(G) in terms of the semigraph parameters. We extend Harary formula for the determinant of the adjacency matrix of graphs to the weighted adjacency matrix of semigraphs. We find bounds for eigenvalues and energy for certain classes of semigraphs.
참고문헌 (15)
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