Abstract
The minimum semidefinite rank of a graph is defined to be the minimum rank among all Hermitian positive semidefinite matrices associated to the graph. A problem of interest is to find upper and lower bounds for
of a graph using known graph parameters such as the independence number and the minimum degree of the graph. We provide a sufficient condition for
of a bipartite graph to equal its independence number. The delta conjecture gives an upper bound for
of a graph in terms of its minimum degree. We present classes of graphs for which the delta conjecture holds.
Acknowledgements
The authors thank the referee for many valuable comments that have improved the quality of this paper. The second author would like to thank Central Michigan University for its support.