📘 graph theory

1. **הבעיה:** נתון גרף מכוון $G = (V, E)$ עם $V = \{0, 1, 2, \ldots, n-1\}$ ו-$m$ קצוות, כאשר לכל קשת יש אורך חיובי. נתון מספר חיובי $k$. יש למצוא לכל קודקוד $i$ את האורך המינימלי

1. **Stating the problem:** We need to understand the theorem of isomorphism for graphs, which states that if two graphs $G$ and $G'$ are isomorphic ($G \cong G'$), then they share

1. **Problem 1: Minimum Spanning Tree (MST) using Kruskal's Algorithm for Graph 1** Given edges and weights, find MST by sorting edges ascending by weight and adding edges without

1. **Stating the problem:** Diberikan dua graf G1 dan G2, kita diminta menentukan apakah kedua graf tersebut isomorfik, yaitu apakah ada pemetaan satu-ke-satu antara simpul-simpul

1. The problem involves analyzing two graphs labeled (a) G and (b) H, each with 10 vertices arranged differently and with distinct edge structures. 2. For graph (a) G, the vertices

1. The problem involves analyzing two graphs, G and H, each with 10 vertices (nodes) and multiple edges connecting these vertices. 2. For graph G, observe the number of vertices $V

1. **Problem Statement:** Determine if the two given undirected graphs (a) G and (b) H are isomorphic. 2. **Definition:** Two graphs are isomorphic if there is a one-to-one corresp

1. The problem is to examine two graphs G and H to determine if they have the same vertices. 2. To check if two graphs have the same vertices, list all vertices of each graph.

1. **Problem Statement:** Determine if the two given planar graphs (a) G and (b) H are isomorphic, meaning they have the same structure in terms of vertices and edges. 2. **Definit

1. **Nyatakan masalah:** Diberikan matriks ketetanggaan graf tidak berarah berukuran 5x5, diminta menggambar dua graf isomorfik yang sesuai dengan matriks tersebut. 2. **Definisi g

1. **Problem Statement:** We have a graph with vertices A, B, C, D, E, F and edges connecting them. We need to verify if the graph is planar using Euler's formula, state why it is

1. **State the problem:** We need to complete the adjacency matrix for a graph with vertices P, Q, R, S, and T. 2. **Recall the adjacency matrix definition:** An adjacency matrix $

1. مسئله: در یک گراف کامل، رابطه 78 = p + q بین مرتبه (p) و اندازه (q) برقرار است. حداقل چند یال باید از این گراف برداشته شود تا گراف به دو گراف کامل تبدیل شود؟ 2. فرمول‌ها و نکات

1. **Problem Statement:** We are given 15 municipalities of Laguna represented as vertices numbered 1 to 15. We need to: - Draw edges between vertices if their municipalities are a

1. **Problem:** Find the number of vertices, edges, and degree of each vertex in graph G. 2. **Step 1: Identify vertices and edges in G.**

1. **Problem Statement:** We need to find the chromatic number of the given graph using the Welch-Powell algorithm, which colors the graph with the minimum number of colors such th

1. Énoncé du problème : Nous avons un graphe non orienté avec 6 nœuds et plusieurs arêtes. La tâche est de décomposer ce graphe en 3 composantes en supprimant une seule arête, en u

1. **Problem Statement:** Show that a complete graph $K_n$ has a Hamiltonian cycle whenever $n \geq 3$. 2. **Definitions:**

1. **Problem Statement:** Determine if the given pairs of graphs (G_5 and G_6, G_7 and G_8) are isomorphic. If yes, provide vertex correspondence and verify edge preservation. If n

1. **Problem Statement:** Find an Euler path in the given graph with vertices O, L, M, K, P, and N and edges as described. 2. **Euler Path Definition:** An Euler path is a trail in

1. The problem asks whether in an Euler path every vertex can only be visited once with no repeats. 2. An Euler path is a path in a graph that visits every edge exactly once.