# Thread: What is a simply connected and 4-connected graph?

1. ## What is a simply connected and 4-connected graph?

I've this question. What is the difference between simply connected graph and a 4-connected graph?

Can anyone kindly help me understand their definition and their difference?

2. ## Re: What is a simply connected and 4-connected graph?

Originally Posted by x3bnm
I've this question. What is the difference between simply connected graph and a 4-connected graph?

Can anyone kindly help me understand their definition and their difference?

Found the answers. Sorry for not researching properly.

The definition of simple graph is given by the text book Discrete Mathematics with Applications second edition by Susanna S. Epp from page 609:

"A simple graph is a graph that does not have any loops or parallel edges."

And the definition of $k$-connected graph is given by k-Connected Graph -- from Wolfram MathWorld

"A graph $G$ is said to be $k$-connected (or $k$-vertex connected, or $k$-point connected) if there does not exist a set of $k-1$ vertices whose removal disconnects the graph, i.e., the vertex connectivity of $G$ is $\geq k$ (Skiena 1990, p. 177). Therefore, a connected graph is $1$-connected, and a biconnected graph is $2$-connected."