Graph energy change due to edge deletion
95 citations recorded by the source corpus.
The energy of a graph is the sum of the singular values of its adjacency matrix. We are interested in how the energy of a graph changes when edges are deleted. Examples show that all cases are possible: increased, decreased, unchanged. Our goal is to find possible graph theoretical descriptions and to provide an infinite family of graphs for each case. The main tool is a singular value inequality for complementary submatrices and its equality case.
Subfields: Computational Theory and Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/21710a0a8f6cc491db6fee8fb70a5f7523ab3a26
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In Geometry and Topology
Citations in the corpus
- Beyond graph energy: norms of graphs and matrices (2015, unknown): “, [2], [9], [10], and [43].”
- Edge addition, singular values, and energy of graphs and matrices (2009, background): “4 of [3], since e is a cut edge, E(G − e) < E(G).”