SPECTRAL PROPERTIES OF EDGE LAPLACIAN MATRIX
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Let N(X) be the Laplacian matrix of a directed graph obtained from the edge adjacency matrix of a graph X. In this work, we study the bipartiteness property of the graph with the help of N(X). We computed the spectrum of the edge Laplacian matrix for the regular graphs, the complete bipartite graphs, and the trees. Further, it is proved that given a graph X, the characteristic polynomial of N(X) divides the characteristic polynomial of N(X′′), where X′′ denote the Kronecker double cover of X.
Abstract
Let N(X) be the Laplacian matrix of a directed graph obtained from the edge adjacency matrix of a graph X. In this work, we study the bipartiteness property of the graph with the help of N(X). We computed the spectrum of the edge Laplacian matrix for the regular graphs, the complete bipartite graphs, and the trees. Further, it is proved that given a graph X, the characteristic polynomial of N(X) divides the characteristic polynomial of N(X′′), where X′′ denote the Kronecker double cover of X.
참고문헌 (13)
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