Characterization of a signed graph whose signed line graph is -consistent.
Characterization of Line-Consistent Signed Graphs
The line graph of a graph with signed edges carries vertex signs. A vertex-signed graph is consistent if every circle (cycle, circuit) has positive vertex-sign product. Acharya, Acharya, and Sinha recently characterized line-consistent signed graphs, i.e., edge-signed graphs whose line graphs, with the naturally induced vertex signature, are consistent. Their proof applies Hoede’s relatively difficult characterization of consistent vertex-signed graphs. We give a simple proof that does not depend...
Cheeger inequalities for unbounded graph Laplacians
We use the concept of intrinsic metrics to give a new definition for an isoperimetric constant of a graph. We use this novel isoperimetric constant to prove a Cheeger-type estimate for the bottom of the spectrum which is nontrivial even if the vertex degrees are unbounded.