By Jurisic A.

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**Extra info for 1-Homogeneous Graphs with Cocktail Party, mu -Graphs**

**Sample text**

7) where v1, v2, 舰,vn are the orthogonal basis, |v1| = |v2| = 舰 = |vn| = 1. If ॕi and ॕj are two distinct eigenvalues of a symmetric matrix A, then their corresponding eigenvectors should be ` vi, vj b = 0. The largest eigenvalue is ॕmax=max॥T舁A॥॥T舁॥ while the smallest eigenvalue is ॕmin=min॥T舁A॥॥T舁॥. A is positive-definite if all the eigenvalues are greater than 0. In a regular graph, the degree of the nodes is an eigenvalue of its matrix adjacency graph. The eigenvalues give rise to a special matrix called a Laplacian matrix, L.

1, there are many circuits. An example is v2 薔 v3 薔 v4 薔 v6 薔 v3 薔 v7 薔 v8 薔 v2 A Hamiltonian path of a graph consists of a path that visits every node in the graph exactly once. 1 is v1 薔 v2 薔 v8 薔 v7 薔 v3 薔 v4 薔 v5 薔 v6 The end points of the Hamiltonian path above are v1 and v6. If the two nodes are adjacent, then the Hamiltonian path becomes a Hamiltonian cycle. 1 does not have any Hamiltonian cycle. Related to the Hamiltonian path is the Eulerian path, which is a path that visits every edge in the graph exactly once.

If the graph does not have a cycle, the graph is an acyclic graph. 3b is acyclic because no cycle exists in it. It is important to note that in an acyclic graph any path between a pair of nodes is unique, whereas in a cyclic graph more than one path may exist between a pair of nodes. A circuit is a cycle that allows the repetitions of nodes but not edges. 1, there are many circuits. An example is v2 薔 v3 薔 v4 薔 v6 薔 v3 薔 v7 薔 v8 薔 v2 A Hamiltonian path of a graph consists of a path that visits every node in the graph exactly once.

### 1-Homogeneous Graphs with Cocktail Party, mu -Graphs by Jurisic A.

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