Minimizing the least eigenvalues of unicyclic graphs with application to spectral spread

By Yi-Zheng Fan, Yi Wang, Yu-Bin Gao. 2008

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The spread of a graph is defined to be the difference between the largest eigenvalue and the least eigenvalue of the adjacency matrix of the graph. Let U k denote the set of connected unicyclic graphs of order n and girth k, and let Un denote the set of connected unicyclic graphs of order n. In this paper, we determine the unique graph with minimum least eigenvalue (respectively, the unique graph with maximum spread) among all graphs in U k. We, finally, characterize the unique graph with minimum least eigenvalue (respectively, the unique graph with maximum spread) among all graphs in Un.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/33a69652f25741d62b39dfdee0db38421cf7b75a