📘 graph theory

1. **State the problem:** Determine if Graph 1 and Graph 2 are isomorphic by comparing vertices, edges, degrees, and connections. 2. **List vertices and edges:**

1. **State the problem:** We have an undirected graph with vertices $a, b, c, d, e, f$ and edges as described. We need to find the degree of each vertex, the total number of edges,

1. **Stating the problem:** We want to understand how to identify the in-degree and out-degree of a vertex in a directed graph. 2. **Definitions:**

1. **State the problem:** We need to determine if the given graph contains a Hamiltonian circuit, which is a cycle that visits every vertex exactly once and returns to the starting

1. **State the problem:** We have a graph with vertices $A$, $B$, $C$, and $D$ arranged as a square with edges $AB$, $BC$, $CD$, $DA$, and diagonals $AC$ and $DB$. We need to find

1. **Problem Statement:** We have a graph with vertices $A, B, C, D, E, F, G$ and edges $A-B, A-D, B-G, D-F, C-D, C-E, E-F, F-G,$ and $D-G$. We need to find:

1. **State the problem:** We have a weighted complete graph with vertices $C, B, A, D, E$ and edges with weights: $C-D=2$, $B-E=9$, $A-E=1$, $B-A=8$, $C-B=15$, $D-E=11$, $C-A=13$,

1. **State the problem:** We need to apply the sorted edges algorithm (also known as the greedy algorithm for the Traveling Salesman Problem) to find a circuit that visits all vert

1. **State the problem:** We need to apply the sorted edges algorithm (also known as the greedy algorithm for the Traveling Salesman Problem) to find a Hamiltonian circuit starting

1. **State the problem:** We need to apply the sorted edges algorithm (also known as the greedy algorithm for the Traveling Salesman Problem) to find a Hamiltonian circuit starting

1. **Problem Statement:** Find the minimum cost spanning tree (MST) of the given weighted undirected graph using Kruskal's algorithm and determine the total cost of the MST.

1. **State the problem:** We need to find the minimum cost spanning tree (MST) of a graph with vertices $\{A,B,C,D,E,F\}$ and edges with weights: $B-E=1$, $A-F=2$, $C-E=4$, $A-E=5$

1. The problem asks to show all valid routes, but no specific context or constraints are given. 2. To solve this, we need more information such as the starting point, destination,

1. **Problem Statement:** We have a 3x3 grid of nine dots. We want to find a path starting at the top-left dot and ending at the bottom-right dot that visits every dot exactly once

1. The user is asking for help to find a thesis topic in the field of graph theory. 2. This is a non-mathematical request related to academic topic selection.

1. The problem is to understand what networks are in graph theory. 2. In graph theory, a network is a graph in which edges have weights or capacities.

1. The problem involves understanding the structure of an 8-spoke radial diagram with a center circle labeled 10 and numbers around it. 2. Each spoke likely represents a connection

1. **State the problem:** Determine which of the given graphs are Eulerian. 2. **Recall the Eulerian graph criteria:**

1. **Stating the problem:** We are asked to find possible traversable paths, Eulerian paths/circuits, and Hamiltonian paths/circuits in the first graph described (top-left graph wi

1. **Nyatakan masalah:** Kita diberi enam bahan kimia A, B, C, D, E, F dan senarai bahan kimia yang tidak boleh disimpan bersama. 2. **Lukis graf mudah:** Setiap bahan kimia diwaki

1. **Énoncé du problème** : L'objectif est d'extraire un sous-graphe complet d'ordre 8 à partir du graphe donné.