// Numbas version: exam_results_page_options
{"name": "Graphs: Match adjacency matrix to a 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: Match adjacency matrix to a graph", "tags": [], "metadata": {"description": "<p>Alternative version of Graphs: Match graph to its adjacency matrix, where the student must match an adjacency matrix to a graph.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>Consider the {number_of_graphs} graphs drawn below, each with vertices labelled from $1$ to $\\var{n+1}$.</p>\n<table style=\"height: 32px; width: 900px;\">\n<tbody>\n<tr style=\"height: 18px;\">\n<td style=\"text-align: center; height: 14px; width: 289.433px;\">Graph $G_1$:</td>\n<td style=\"text-align: center; width: 281.05px; height: 14px;\">Graph $G_2$:</td>\n<td style=\"text-align: center; width: 281.05px; height: 14px;\">Graph $G_3$:</td>\n</tr>\n<tr style=\"height: 18px;\">\n<td style=\"text-align: center; height: 18px; width: 289.433px;\">{graphs[0]}</td>\n<td style=\"text-align: center; width: 281.05px; height: 18px;\">{graphs[1]}</td>\n<td style=\"text-align: center; width: 281.05px; height: 18px;\">{graphs[2]}</td>\n</tr>\n</tbody>\n</table>\n<p>You will be shown an adjacency matrix below. The $i$th row or column of the matrix corresponds to vertex labelled $i$.</p>\n<p>Match the matrix to the graph it describes the adjacency of.</p>", "advice": "<p>The adjacency matrix $M$ of a graph $G$ has $(i,j)$th entry $1$ whenever there is an edge from vertex $i$ to vertex $j$.</p>\n<p>The $(i,j)$th entry is $0$ otherwise.</p>", "rulesets": {}, "extensions": ["graph-theory-v1"], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"graphs": {"name": "graphs", "group": "Ungrouped variables", "definition": "map(\n  draw_graph_from_adjacency(matrices[q], map(string(i), i, 1..n+1)), \n  q, 0..number_of_graphs - 1\n)", "description": "<p>Graphs built fron the adjacency matrices</p>", "templateType": "anything", "can_override": false}, "matrices": {"name": "matrices", "group": "Ungrouped variables", "definition": "map(\n  matrix(reorder(  \n    [reorder(a[q][0], vertex_perm)] +\n    map(\n      reorder(map(a[q][i][j-i], i, 0..j-1) + a[q][j], vertex_perm), j, 1..n\n      ), vertex_perm\n    )), q, 0..number_of_graphs - 1\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>", "templateType": "anything", "can_override": false}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "map(\n  [first_row[q]] +\n  map([0] + repeat(random(0,0,0,1,1), n-j), j, 1..n-1)\n  + [[0]],\n  q, 0..number_of_graphs - 1\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}, "number_of_graphs": {"name": "number_of_graphs", "group": "Ungrouped variables", "definition": "3", "description": "<p>The number of graphs displayed in the question. Each adjacency matrix correctly matched to its graph will score a point.</p>\n<p>This must be less than or equal to the number of vertices n+1.</p>", "templateType": "anything", "can_override": false}, "graph_mat_pairs": {"name": "graph_mat_pairs", "group": "Ungrouped variables", "definition": "shuffle(\n  map(\n    [\n      'graph': graphs[i],\n      'matrix': matrices[i],\n      'marks': 4*id(number_of_graphs)[i]\n    ], i, 0..number_of_graphs - 1\n  )\n)", "description": "<p>The graphs, matched with their adjacency matrices. The 'marks' column will form the marking matrix</p>", "templateType": "anything", "can_override": false}, "first_row": {"name": "first_row", "group": "Ungrouped variables", "definition": "shuffle(\n  flatten(map(\n    map(vector(id(n+1)[i]) + vector(id(n+1)[j]), j, i+1..n), i, 1..n)\n  )\n)", "description": "<p>To ensure no two adjacency matrices are the same, the first row will be taken from this list.</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": ["graphs", "matrices", "n", "a", "number_of_graphs", "graph_mat_pairs", "first_row", "vertex_perm"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "1_n_2", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>$A = \\var{graph_mat_pairs[0]['matrix']}$.</p>\n<p>Select which graph $A$ is the adjacency matrix for.</p>", "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["$G_1$", "$G_2$", "$G_3$"], "matrix": "graph_mat_pairs[0]['marks']"}], "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": "Chris Graham", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/369/"}, {"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": "Chris Graham", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/369/"}, {"name": "Sam Mutter", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/9360/"}]}