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On graphs and algebraic graphs that do not contain cycles of length 4
2010
Journal of Graph Theory
We consider extremal problems for algebraic graphs, that is, graphs whose vertices correspond to vectors in R d , where two vectors are connected by an edge according to an algebraic condition. We also derive a lower bound on the rank of the adjacency matrix of a general abstract graph using the number of 4-cycles and a parameter which measures how close the graph is to being regular. From this we derive a rank bound for the adjacency matrix A of any simple graph with n vertices and E edges
doi:10.1002/jgt.20542
fatcat:fkjquevm3bag7n4f5b6wzf4dum