Question

This question for Discrete Math course. All of them about the same topic!!

Give me a simple definition of each one:

1) Neigbhor of a vertex

2) A connected graph

3) Length of cycle

4) Euler walk

5) Planar graph

6) Chromatic member of graph

7) X(G)

Answer 1

1) Neighbor of a vertex: In a graph G if v is a vertex then vertices which are adjacent to v are neighbor of vertex v.

2) A connected Graph :

A   graph is said to be connected  if there exist a path between every pair of vertices.A connected graph has only one component.

3)Length of a cycle:

A cycle is a path of edges and vertices wherein the vertices and edges are not repeated expect the first and last vertex

Number of edges in any cycle is called as length of the cycle.

4)Euler walk:

An Eulerian walk in an undirected graph is a walk that uses each edge exactly once.

5)Planar Graph:

A graph is said to be planar graph if it can be drawn on the plane with no intersecting edges.

6)Chromatic number of graph:

The chromatic number of a graph is the smallest number of colors needed to color the vertices of a graph so that no two adjacent vertices have the same color .

7)X(G):  

X(G) is Chromatic number of a graph whose definition is written above.