The Spectral Radius for a Class of Double-Star-Like Tree Systems with Maximal Degree 4

الملخص EN

We mainly study the properties of the 4-double-star-like tree, which is the generalization of star-like trees.

Firstly we use graft transformation method to obtain the maximal and minimum extremal graphs of 4-double-star-like trees.

Secondly, by the relations between the degree and second degree of vertices in maximal extremal graphs of 4-double-star-like trees we get the upper bounds of spectral radius of 4-double-star-like trees.