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On the minimum rank of the join of graphs and decomposable graphs

✍ Scribed by Francesco Barioli; Shaun Fallat

Publisher
Elsevier Science
Year
2007
Tongue
English
Weight
184 KB
Volume
421
Category
Article
ISSN
0024-3795

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✦ Synopsis

For a given undirected graph G, the minimum rank of G is defined to be the smallest possible rank over all real symmetric matrices A whose (i, j )th entry is nonzero whenever i / = j and {i, j } is an edge in G. In this work we consider joins and unions of graphs, and characterize the minimum rank of such graphs in the case of 'balanced inertia'. Several consequences are provided for decomposable graphs, also known as cographs.

πŸ“œ SIMILAR VOLUMES

On the join of graphs and chromatic uniq
On the join of graphs and chromatic uniqueness
✍ G. L. Chia πŸ“‚ Article πŸ“… 1995 πŸ› John Wiley and Sons 🌐 English βš– 519 KB

## Abstract A graph is chromatically unique if it is uniquely determined by its chromatic polynomial. Let __G__ be a chromatically unique graph and let __K__~__m__~ denote the complete graph on __m__ vertices. This paper is mainly concerned with the chromaticity of __K__~__m__~ + __G__ where + deno