# Graphs, groups, and more: celebrating Brian Alspach’s 80th and Dragan Marušič’s 65th birthdays

28 May 2018 to 1 June 2018
Koper
UTC timezone

## Edge perturbations on signed graphs with clusters

Not scheduled
15m
UP FHS (Koper)

### UP FHS

#### Koper

Titov trg 5,Koper

### Speaker

Dr Maurizio Brunetti (Università di Napoli)

### Description

Let $\Gamma$ be a signed graph. A cluster in $\Gamma$ of order $c$ and degree $s$, is a pair of vertex subset $(C,S)$, where $C$ is a set of cardinality $c \geq 2$ of pairwise co-neighbor vertices sharing the same set of $s$ neighbors and all edges connecting a fixed vertex in $C$ are equallly signed. We consider the graph $\Gamma(H)$ which is obtained from $G$ by identifying $V(H)$ with $C$ and show that some Laplacian or Adjacency eigenvalues of $\Gamma(H)$ remain the same whatever $H$ we choose in a suitable set of signed graphs. Such techniques also provide a generalization to signed contexts of the Faria’s lower bound on the multiplicity of the Laplacian eigenvalue 1 of a graph with pendant vertices.

### Primary author

Dr Maurizio Brunetti (Università di Napoli)

### Co-author

Francesco Belardo (University of Naples Federico II)

### Presentation Materials

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