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Mathematics Homework Solutions
#28050
Find the values of alpha and omega for the two graphs given in the attached file (45.4.doc).
The stability number, alpha(G), of a graph G is the cardinality of the largest subset S of V(G), the vertex set of G, such that no two of the vertices in S are connected by an edge of G.
The clique number, omega(G), of a graph G is the cardinality of the largest subset S of V(G), the vertex set of G, such that every pair of vertices in S are connected by an edge of G.
Two graphs, G and H, are given as figures in an attached .doc file (45.4.doc). Find the values of alpha(G), omega(G), alpha(H), and omega(H).
Graphs G and H are given in an attached .doc file (45.4.doc). Solutions, with detailed justifications, are provided in another attached .doc file (Graphs-Alpha&Omega-Solution.doc). The statement of the problem and the given graphs are included in the latter file.
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