### Graph Theory Problem - Adjacency and Incidence #### Problem Statement: Consider the graph in **Figure 1**. Which of the following statements hold true for the graph?  #### Figure Description: In Figure 1, the graph consists of: - **Vertices**: \( v_1, v_2, v_3, v_4 \) - **Edges**: \( e_1, e_2, e_3, e_4, e_5, e_6, e_7 \) The edges are connected as follows: - Edge \( e_1 \) connects vertex \( v_1 \) to vertex \( v_3 \). - Edge \( e_2 \) connects vertex \( v_3 \) to vertex \( v_4 \). - Edge \( e_3 \) connects vertex \( v_2 \) to vertex \( v_4 \). - Edge \( e_4 \) connects vertex \( v_1 \) to vertex \( v_2 \). - Edge \( e_5 \) connects vertex \( v_1 \) to vertex \( v_4 \). - Edge \( e_6 \) connects vertex \( v_3 \) to vertex \( v_4 \). - Edge \( e_7 \) forms a loop at vertex \( v_2 \). #### Statements to Evaluate: (a) Vertices \( v_3 \) and \( v_2 \) are adjacent (b) Edge \( e_6 \) is incident with vertex \( v_4 \) (c) Vertex \( v_2 \) is incident with edge \( e_4 \) (d) Vertex \( v_4 \) and edges \( e_5 \) and \( e_6 \) form a subgraph of the graph **Figure 1: Graph for Problem 1** ### Analysis: 1. **Adjacency**: Vertices \( v_3 \) and \( v_2 \) are not adjacent; there is no direct edge connecting them. 2. **Incidence with \( v_4 \)**: Edge \( e_6 \) connects vertex \( v_1 \) to vertex \( v_4 \), making it incident with \( v_4 \). 3. **Incidence with \( v_2 \)**: Edge \( e_4 \) connects vertex \( v_1

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‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements are distributed horizontally in the form of rows, and vertically in the form of columns.