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Distance Matrix of a Tree

Part of the Universitext book series (UTX)

Let G be a connected graph with V(G) = {1,⋯n}. Recall that the distance d(i, j) between the vertices i and j of G is the length of a shortest path from i to j. The distance matrix D(G) of G is an n×n matrix with its rows and columns indexed by V(G). For ij, the (i, j)-entry di j of G is set equal to d(i, j): Also, d ii = 0, i = 1,⋯n. We will often denote D(G) simply by D. Clearly, D is a symmetric matrix with zeros on the diagonal. The distance, as a function on V(GV(G), satisfies the triangle inequality. Thus, for any vertices i, j and k.

Keywords

Distance Matrix Connected Graph Algebraic Multiplicity Unicyclic Graph Pendant Vertex 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References and Further Reading

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© Hindustan Book Agency (India) 2010

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