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| Paper IPM / M / 8425 |
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| Abstract: | |||||||
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Let G be a graph of order n and rank(G) denotes the rank of
its adjacency matrix. Clearly, n \leqslant rank (G) + rank
―G \leqslant 2n. In this paper we characterize all
graphs G such that rank(G) + rank(―G) = n, n + 1
or n + 2.
Also for every integer n \geqslant 5 and any k, 0\leqslant k \leqslant n, we
construct a graph G of order n, such that rank(G) + rank (―G) = n + k.
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