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### Characterization of Line-Consistent Signed Graphs

Discussiones Mathematicae Graph Theory

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...

### Glossary of signed and gain graphs and allied areas.

The Electronic Journal of Combinatorics [electronic only]

### Periodicity in quasipolynomial convolution.

The Electronic Journal of Combinatorics [electronic only]

### The Dynamics of the Forest Graph Operator

Discussiones Mathematicae Graph Theory

In 1966, Cummins introduced the “tree graph”: the tree graph T(G) of a graph G (possibly infinite) has all its spanning trees as vertices, and distinct such trees correspond to adjacent vertices if they differ in just one edge, i.e., two spanning trees T1 and T2 are adjacent if T2 = T1 − e + f for some edges e ∈ T1 and f ∉ T1. The tree graph of a connected graph need not be connected. To obviate this difficulty we define the “forest graph”: let G be a labeled graph of order α, finite or infinite,...

### Six little squares and how their numbers grow.

Journal of Integer Sequences [electronic only]

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