In this paper, it is shown that among connected graphs with maximum clique size ω, the minimum value of the spectral radius of adjacency matrix is attained for a kite graph PKn−ω,ω , which consists of a complete graph Kω to a vertex of which a path Pn−ω is attached. For any fixed ω, a small interval to which the spectral radii of kites PKm,ω , m ≥ 1, belong is exhibited.

We show that the kite graph $K_4^{(n)}$ uniquely maximizes distance spectral radius among all connected $4$-chromatic planar graphs on $n$ vertices.

In this paper, it is shown that among connected graphs with maximum clique size ω, the minimum value of the spectral radius of adjacency matrix is attained for a kite graph PKn−ω,ω , which consists of a complete graph Kω to a vertex of which a path Pn−ω is attached. For any fixed ω, a small interval to which the spectral radii of kites PKm,ω , m ≥ 1, belong is exhibited.

Novel and Nontraditional Data Streams: Where Do They Fit into Biosurveillance Action? Laura Streichert*1, Aaron Kite-Powell2, Timothy J. Dasey2, Richard Hopkins3, 1, Courtney Corley4 and Steve Bennett5 1International Society for Disease Surveillance, Brighton, MA, USA; 2MIT Lincoln Laboratory, Lexington, MA, USA; 3University of Florida, Gainesville, FL, USA; 4Pacific Northwest National Laborato...

We characterize the planar central configurations of the 4body problem with masses m1 = m2 ̸= m3 = m4 which have an axis of symmetry. It is known that this problem has exactly two classes of convex central configurations, one with the shape of a rhombus and the other with the shape of an isosceles trapezoid. We show that this 4-body problem also has exactly two classes of concave central configu...