On algebraic connectivity and spectral integral variations of graphs
- Barik, Sasmita
- Pati, Sukanta
DOIAbstract
AbstractLet G be a simple connected graph and L(G) be the Laplacian matrix of G. Let a(G) be the second smallest eigenvalue of L(G). An eigenvector of L(G) corresponding to the eigenvalue a(G) is called a Fiedler vector of G. Let Y be a Fiedler vector of G. A characteristic vertex is a vertex u of G such that Y(u)=0 and such that there is a vertex w adjacent to u satisfying Y(w)≠0. A characteristic edge is an edge {u,v} such that Y(u)Y(v)<0. The characteristic set S is the collection of all characteristic vertices and characteristic edges of G with respect to Y. A Perron branch at S is a connected component of G⧹S with the smallest eigenvalue of the corresponding principal submatrix of L(G) less than or equal to a(G). Suppose that S contain...
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