Radius-invariant graphs

On critical and cocritical radius edge-invariant graphs

The concepts of critical and cocritical radius edge-invariant graphs are introduced. We prove that every graph can be embedded as an induced subgraph of a critical or cocritical radius-edge-invariant graph. We show that every cocritical radius-edge-invariant graph of radius r ≥ 15 must have at least 3r + 2 vertices.

On graphs whose spectral radius

The structure of graphs whose largest eigenvalue is bounded by 3 2 √ 2 (≈ 2.1312) is investigated. In particular, such a graph can have at most one circuit, and has a natural quipu structure.

Spectral radius of bipartite graphs

Radius-forcing sets in graphs

Let G be a connected graph of order p and let 0 ::f. s ~ V ( G). Then S is a rad(G)-forcing set (or a radius-forcing set of G) if, for each v E V(G), there exists v' E S with dc(v, v') ?: rad(G). The cardinality of a smallest radius-forcing set of G is called the radius-forcing number of G and is denoted by rf(G). A graph G is called a randomly k-forcing graph for a positive integer k if every ...

Invariant Tensors and Graphs

We describe a correspondence between GLn-invariant tensors and graphs. We then show how this correspondence accommodates various types of symmetries and orientations.