grandes-ecoles 2024 Q9

grandes-ecoles · France · mines-ponts-maths2__mp Matrices Eigenvalue and Characteristic Polynomial Analysis
Determine the characteristic polynomial of the double star with $d _ { 1 } + d _ { 2 } + 2$ vertices, consisting respectively of two disjoint stars with $d _ { 1 }$ and $d _ { 2 }$ branches, to which an additional edge has been added connecting the two centers of the two stars. What is the rank of the adjacency matrix of this double star? 
Determine the characteristic polynomial of the double star with $d _ { 1 } + d _ { 2 } + 2$ vertices, consisting respectively of two disjoint stars with $d _ { 1 }$ and $d _ { 2 }$ branches, to which an additional edge has been added connecting the two centers of the two stars.\\
What is the rank of the adjacency matrix of this double star?
Paper Questions
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