In Class Test

Find the adjacency matrix, its squire and cube of the following graph $G$.

How many walks from $v_1$ to $v_2$ of length $3$?

List all such walks one by one.

In Class Test - 18

Calculate all Laplacian eigenpairs of the following graph $G$.

In Class Test

Let $G$ be the following graph. Find the characteristic polynomial of $A(G)$. Verify Theorem 1.8.

In Class Test

Find the characteristic polynomial of adjacent matrix of the following graph by Theorem 1.12, 1.14 and 1.17.

In Class Test

Find the characteristic polynomial of adjacent matrix of the following graph by Theorem 1.7, 1.17 and 1.18.

In Class Test

Consider the following graph G and Corollary 1.26. Suppose $q(\mu) = (\mu^2 - \alpha)(\mu^3 - 3)(\mu + b), a,b>0$ and $q(A(G)) = 24J$. Find the spectrum of the graph.

In Class Test

Consider the following graph $G$. Find $q(\mu)$ in Corollary 1.26 and the spectrum of $G$.

In Class Test - 7

Let $\lambda$ be an eigenvalue of the adjacency matrix of a line graph of $G$. Show that $\lambda \geq 2$.