ALGORITHMIC PROOF OF MaxMult(T) = p(T) Kim, In-Jae;
For a given graph G we consider a set S(G) of all symmetric matrices A =  whose nonzero entries are placed according to the location of the edges of the graph, i.e., for , if and only if vertex is adjacent to vertex . The minimum rank mr(G) of the graph G is defined to be the smallest rank of a matrix in S(G). In general the computation of mr(G) is complicated, and so is that of the maximum multiplicity MaxMult(G) of an eigenvalue of a matrix in S(G) which is equal to - mr(G) where n is the number of vertices in G. However, for trees T, there is a recursive formula to compute MaxMult(T). In this note we show that this recursive formula for MaxMult(T) also computes the path cover number (T) of the tree T. This gives an alternative proof of the interesting result, MaxMult(T) = (T).
maximum corank;maximum multiplicity;minimum rank;path cover number;tree;
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