RELATION BETWEEN CHROMATIC NUMBER OF HYPERGRAPHS AND LARGEST EIGENVALUE OF HYPERMATRICES
Hypergraph is a generalization of the graph, that is one edge of the hypergraph can connect more than two vertices. Coloring on hypergraph is defined as the color on each vertex of the hypergraph such that there are at least two different colors in one edge. While the chromatic numbers on hypergr...
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| Format: | Theses |
| Language: | Indonesia |
| Online Access: | https://digilib.itb.ac.id/gdl/view/44541 |
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| Institution: | Institut Teknologi Bandung |
| Language: | Indonesia |
| Summary: | Hypergraph is a generalization of the graph, that is one edge of the hypergraph can
connect more than two vertices. Coloring on hypergraph is defined as the color on
each vertex of the hypergraph such that there are at least two different colors in one
edge. While the chromatic numbers on hypergraph is the minimum number of
colors to color the hypergraph.
Uniform hypergraph is a hypergraph that each edge connecting the vertices by the
same amount. Adjacency of uniform hypergraph can be encoded into hipermatrix
and will be called as adjacency hipermatrix. The largest eigenvalue of hypergraph
is the largest eigenvalue of its adjacency hipermatrix. The relationship between the
largest eigenvalue of adjacency matrix of graph and its chromatic number remain
fulfilled for the largest eigenvalue of adjacency hipermatrix of hypergraph and its
chromatic number. |
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