Fiedler vector analysis for particular cases of connected graphs

TL;DR

This paper investigates the properties of Fiedler vectors in specific subclasses of connected block graphs, focusing on their algebraic connectivity and introducing new graph families.

Contribution

It introduces two new families of block graphs and analyzes their Fiedler vectors and algebraic connectivity in particular cases.

Findings

Fiedler vectors exhibit specific behaviors in block-path and block-starlike graphs.

Algebraic connectivity varies systematically in the studied graph subclasses.

Classification cases reveal distinct spectral properties.

Abstract

In this paper, some subclasses of block graphs are considered in order to analyze Fiedler vector of its members. Two families of block graphs with cliques of fixed size, the block-path and block-starlike graphs, are introduced. Cases A and B of classification for both families were considered, as well as the behavior of the algebraic connectivity for particular cases of block-path graphs.