// Numbas version: exam_results_page_options
{"name": "Graphs: Write the adjacency matrix of this graph", "extensions": ["graph-theory-v1"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Graphs: Write the adjacency matrix of this graph", "tags": [], "metadata": {"description": "<p>The student is shown one graph, and asked to type the adjacency matrix</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>You will be shown three graphs below, each with vertices labelled from $1$ to $\\var{n+1}$.</p>\n<p>Consider the following graph:</p>\n<p>{max_width(30,graph)}</p>\n<p>Write down the adjacency matrix of this graph.</p>\n<p>The $i$th row or column of your matrix should correspond to the vertex labelled $i$.</p>", "advice": "<p>The adjacency matrix $M$ of a graph $G$ has $ij$th entry $1$ whenever there is an edge from vertex $i$ to vertex $j$.</p>\n<p>The $ij$th entry is $0$ otherwise.</p>", "rulesets": {}, "extensions": ["graph-theory-v1"], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"graph": {"name": "graph", "group": "Ungrouped variables", "definition": "draw_graph_from_adjacency(mat, map(string(i), i, 1..n+1))", "description": "<p>Graphs built fron the adjacency matrices</p>", "templateType": "anything", "can_override": false}, "mat": {"name": "mat", "group": "Ungrouped variables", "definition": "matrix(reorder(  \n    [reorder(a[0], vertex_perm)] +\n    map(\n      reorder(map(a[i][j-i], i, 0..j-1) + a[j], vertex_perm), j, 1..n\n      ), vertex_perm\n  ))", "description": "<p>The qth matrix takes entries from a[q] as its upper triangle, then duplicates this for the bottom triangle to make a symmetric matrix.</p>", "templateType": "anything", "can_override": false}, "n": {"name": "n", "group": "Ungrouped variables", "definition": "7", "description": "<p>Each graph will contain n+1 vertices.</p>\n<p>n should be at least 4. My view is that it looks good when n is around 7 to 8.</p>", "templateType": "anything", "can_override": false}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "map([0] + repeat(random(0,0,0,1,1), n-j), j, 0..n-1)\n+ [[0]]\n", "description": "<p>The top-right triangle of the adjacency matrices. The bottom-left triangle will be the transpose of this, so that the matrices are symmetrical.</p>\n<p>The first rows are all distinct, so no two adjacency matrices are the same.</p>\n<p>Change the number of 0s and 1s to get a more/less dense matrix.</p>", "templateType": "anything", "can_override": false}, "vertex_perm": {"name": "vertex_perm", "group": "Ungrouped variables", "definition": "shuffle(0..n)", "description": "<p>The labels of vertices will be permuted. This is so it isn't obvious that the first row of the adjacency matrices are different.</p>", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["n", "a", "vertex_perm", "graph", "mat"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "matrix", "useCustomName": false, "customName": "", "marks": "4", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "correctAnswer": "{mat}", "correctAnswerFractions": false, "numRows": "{n+1}", "numColumns": "{n+1}", "allowResize": false, "tolerance": 0, "markPerCell": true, "allowFractions": false, "minColumns": 1, "maxColumns": 0, "minRows": 1, "maxRows": 0}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Sam Mutter", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/9360/"}]}]}], "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Sam Mutter", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/9360/"}]}