Geodesic
Algebraic connectivity of $k$-connected graphs
Czechoslovak Mathematical Journal, Tome 65 (2015) no. 1, pp. 219-236

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Let $G$ be a $k$-connected graph with $k \ge 2$. A hinge is a subset of $k$ vertices whose deletion from $G$ yields a disconnected graph. We consider the algebraic connectivity and Fiedler vectors of such graphs, paying special attention to the signs of the entries in Fiedler vectors corresponding to vertices in a hinge, and to vertices in the connected components at a hinge. The results extend those in Fiedler's papers Algebraic connectivity of graphs (1973), A property of eigenvectors of nonnegative symmetric matrices and its application to graph theory (1975), and Kirkland and Fallat's paper Perron Components and Algebraic Connectivity for Weighted Graphs (1998).
DOI : 10.1007/s10587-015-0170-9
Classification : 05C50, 15A18
Keywords: algebraic connectivity; Fiedler vector 
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Kirkland, Steve; Rocha, Israel; Trevisan, Vilmar. Algebraic connectivity of $k$-connected graphs. Czechoslovak Mathematical Journal, Tome 65 (2015) no. 1, pp. 219-236. doi: 10.1007/s10587-015-0170-9

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