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Composite Relations




Q. What is the composite of the relations R and S, where R is the relation from {1, 2, 3} to {1, 2, 3, 4} with R = {(1, 1), (1, 4), (2, 3), (3, 1), (3, 4)} and S is the relation from {1, 2, 3, 4} to {0, 1, 2} with S = {(1, 0), (2, 0), (3, 1), (3, 2), (4, 1)}?




n-ary Relations and Their Applications





Equivalence Relations




Q. Let R be the relation on the set of real numbers such that aRb if and only if a − b is an integer. Is R an equivalence relation?



Q. Suppose that R is the relation on the set of strings of English letters such that aRb if and only if l(a) = l(b), where l(x) is the length of the string x. Is R an equivalence relation?



Equivalence Classes



Q. Let R be the relation on the set of real numbers such that aRb if and only if a − b is an integer. What is the equivalence class of an integer for the equivalence relation ?




Graphs





Graph Terminology and Special Types of Graphs




Complete Graphs



Cycles, Wheels and n - cubes (n-dimensional hypercube)




Bipartite Graphs





Matching, Maximum matching and Complete matching




Example : Maximum matching and Complete matching




Isomorphism of Graphs




Determining whether Two Simple Graphs are Isomorphic



Q. Check if the graphs in Figure 9 and 10 are isomorphic.



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