Subgraph identification

Questions asking to identify or draw subgraphs with specific properties (trees, simple-connected, etc.) from a given graph.

2 questions · Easy -1.2

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AQA Further AS Paper 2 Discrete 2022 June Q1
2 marks Easy -1.2
1 The connected graph \(G\) is shown below. \includegraphics[max width=\textwidth, alt={}, center]{ecbeedf5-148e-40ad-b8a2-a7aa3db4a115-02_542_834_630_603} The graphs \(A\) and \(B\) are subgraphs of \(G\) Both \(A\) and \(B\) have four vertices. 1
  1. The graph \(A\) is a tree with \(x\) edges.
    State the value of \(x\) Circle your answer. 3459 1
  2. The graph \(B\) is simple-connected with \(y\) edges.
    Find the maximum possible value of \(y\) Circle your answer. 3459
AQA Further AS Paper 2 Discrete 2023 June Q1
1 marks Easy -1.2
1 The graph \(G\) has 8 vertices and 13 edges as shown in the diagram below. \includegraphics[max width=\textwidth, alt={}, center]{372edcfa-c3cd-4c83-89e9-2bb5fd9825f1-03_494_392_482_806} Graph \(H\) is a simple-connected subgraph of graph \(G\) Which of the following diagrams could represent graph \(H\) ? Tick ( ✓ ) one box. \includegraphics[max width=\textwidth, alt={}, center]{372edcfa-c3cd-4c83-89e9-2bb5fd9825f1-03_312_310_1354_351} \includegraphics[max width=\textwidth, alt={}, center]{372edcfa-c3cd-4c83-89e9-2bb5fd9825f1-03_321_310_1676_351} \includegraphics[max width=\textwidth, alt={}, center]{372edcfa-c3cd-4c83-89e9-2bb5fd9825f1-03_117_115_1448_822} \includegraphics[max width=\textwidth, alt={}, center]{372edcfa-c3cd-4c83-89e9-2bb5fd9825f1-03_312_310_2014_351} \includegraphics[max width=\textwidth, alt={}, center]{372edcfa-c3cd-4c83-89e9-2bb5fd9825f1-03_122_117_1777_822} \includegraphics[max width=\textwidth, alt={}, center]{372edcfa-c3cd-4c83-89e9-2bb5fd9825f1-03_314_314_2343_349} \includegraphics[max width=\textwidth, alt={}, center]{372edcfa-c3cd-4c83-89e9-2bb5fd9825f1-03_120_115_2108_822}