Fix DFS root-revisit bug in isConnected; add Prufer sequence report

Issue #41: AlgorithmUtils.isConnected never marked the root node as
visited before calling dfs, so any neighbor of node 0 would see
parent[0]==-1 and re-enter node 0, causing redundant traversal and
potential StackOverflowError on large dense graphs. Fix: set parent[0]=0
before the dfs call.

Issue #38: Add PruferSequence report extension under basicreports.
Repeatedly removes the leaf with the smallest vertex id and appends its
neighbor's id to build the n-2 length Prufer sequence of a labeled tree.
Returns an error string if the graph is not a tree.

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

Author: rostam

src/graphtea/extensions/AlgorithmUtils.java

@@ -53,6 +53,7 @@ public static boolean isConnected(GraphModel g) {
         for (int i = 0; i < g.getVerticesCount(); i++) {
             parent[i] = -1;
         }
+        parent[0] = 0; // mark root as visited so it is not re-entered during recursion
         dfs(g, 0, vs, parent);
         return vs.stream().distinct().count() == g.getVerticesCount();
     }

src/graphtea/extensions/reports/basicreports/PruferSequence.java

@@ -0,0 +1,100 @@
+// GraphTea Project: http://github.com/graphtheorysoftware/GraphTea
+// Copyright (C) 2012 Graph Theory Software Foundation: http://GraphTheorySoftware.com
+// Copyright (C) 2008 Mathematical Science Department of Sharif University of Technology
+// Distributed under the terms of the GNU General Public License (GPL): http://www.gnu.org/licenses/
+
+package graphtea.extensions.reports.basicreports;
+
+import graphtea.graph.graph.GraphModel;
+import graphtea.graph.graph.Vertex;
+import graphtea.platform.lang.CommandAttitude;
+import graphtea.plugins.reports.extension.GraphReportExtension;
+
+
+/**
+ * Computes the Prüfer sequence of a labeled tree.
+ *
+ * The Prüfer sequence is a unique sequence of n-2 vertex labels that encodes
+ * a labeled tree on n vertices. It is produced by repeatedly removing the leaf
+ * with the smallest label and appending its neighbor's label to the sequence.
+ *
+ * The graph must be an unrooted labeled tree (connected, undirected, n-1 edges).
+ */
+@CommandAttitude(name = "prufer_sequence", abbreviation = "_ps")
+public class PruferSequence implements GraphReportExtension<String> {
+
+    public String calculate(GraphModel g) {
+        int n = g.getVerticesCount();
+        if (n < 2) {
+            return "Graph must have at least 2 vertices";
+        }
+        if (g.getEdgesCount() != n - 1) {
+            return "Graph is not a tree (edge count must equal n-1)";
+        }
+
+        // degree[i] mirrors the current degree of vertex with id=i
+        int[] degree = new int[n];
+        Vertex[] vertices = g.getVertexArray();
+        for (Vertex v : vertices) {
+            degree[v.getId()] = g.getDegree(v);
+        }
+
+        int[] sequence = new int[n - 2];
+        boolean[] removed = new boolean[n];
+
+        for (int step = 0; step < n - 2; step++) {
+            // find the leaf with the smallest id
+            int leaf = -1;
+            for (int i = 0; i < n; i++) {
+                if (!removed[i] && degree[i] == 1) {
+                    leaf = i;
+                    break;
+                }
+            }
+            if (leaf == -1) {
+                return "Graph is not a tree (cycle detected)";
+            }
+
+            // find the unique neighbor of this leaf
+            Vertex leafVertex = g.getVertex(leaf);
+            int neighbor = -1;
+            for (Vertex nb : g.getNeighbors(leafVertex)) {
+                if (!removed[nb.getId()]) {
+                    neighbor = nb.getId();
+                    break;
+                }
+            }
+            if (neighbor == -1) {
+                return "Graph is not a tree (disconnected)";
+            }
+
+            sequence[step] = neighbor;
+            removed[leaf] = true;
+            degree[leaf] = 0;
+            degree[neighbor]--;
+        }
+
+        // format as comma-separated list of 1-based labels for readability
+        StringBuilder sb = new StringBuilder();
+        for (int i = 0; i < sequence.length; i++) {
+            sb.append(sequence[i]);
+            if (i < sequence.length - 1) {
+                sb.append(", ");
+            }
+        }
+        return sb.toString();
+    }
+
+    public String getName() {
+        return "Prufer Sequence";
+    }
+
+    public String getDescription() {
+        return "Prufer sequence of a labeled tree";
+    }
+
+    @Override
+    public String getCategory() {
+        return "General";
+    }
+}