In this work we present some property about graph connectivity. Let G be a finite undirected graph, with no loops or multiple edges and L the Laplacian matrix of G, with eingevalues . In their paper Anderson and Morley (see Anderson & Morley, 1985 ) identify the number of components of G with the multiplicity of . Since then many other results about connectivity have been obtained; in (Berge, 1991), (Stefani & Torriero, 2001) some sufficient conditions for a graph to be connected depending on degrees of G are given. We extend a result obtained in (Stefani & Torriero, 2001) for regular graphs; then we propose some new sufficient conditions for a graph to be connected.
Grassi, R. (2004). Relevant inequalities in graph connectivity. ARCHIVES OF INEQUALITIES AND APPLICATIONS, 2, 183-198.
Relevant inequalities in graph connectivity
GRASSI, ROSANNA
2004
Abstract
In this work we present some property about graph connectivity. Let G be a finite undirected graph, with no loops or multiple edges and L the Laplacian matrix of G, with eingevalues . In their paper Anderson and Morley (see Anderson & Morley, 1985 ) identify the number of components of G with the multiplicity of . Since then many other results about connectivity have been obtained; in (Berge, 1991), (Stefani & Torriero, 2001) some sufficient conditions for a graph to be connected depending on degrees of G are given. We extend a result obtained in (Stefani & Torriero, 2001) for regular graphs; then we propose some new sufficient conditions for a graph to be connected.
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