Some universal graphs
Given a graph G with vertex set V (G) = {x1, x2, . . . , xn}, we define the adjacency matrix of G to be the matrix A(G) = [aij ] where aij = 1 if xi and xj are adjacent in G. From the set of all adjacency matrices of G, denoted by A (G), we then form the subspace spanned by this set, denoted by (A (...
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| Main Authors: | , |
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| Format: | text |
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Animo Repository
2009
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| Online Access: | https://animorepository.dlsu.edu.ph/faculty_research/11218 |
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| Institution: | De La Salle University |
| Summary: | Given a graph G with vertex set V (G) = {x1, x2, . . . , xn}, we define the adjacency matrix of G to be the matrix A(G) = [aij ] where aij = 1 if xi and xj are adjacent in G. From the set of all adjacency matrices of G, denoted by A (G), we then form the subspace spanned by this set, denoted by (A (G)). A graph with adjacency matrix H is said to be a G-descendant if H ∈ (A (G)). If G is of order n and all graphs of order n are G-descendants, we say that G is universal. In this paper, we show that complements of some universal graphs are also universal. |
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