How many edges, respectively, the Harary graphs $H_{50,52}$ and $H_{51,52}$ have?
1300 and 1325
1300 and 1326
2600 and 2625
2600 and 2626
Smallest number of edges of $H_{k,n}$ is ⌈$\frac{k \cdot n}{2}$⌉.
Which of the following statements is FALSE?
A planar graph with ten vertices and nine edges has exactly one region.
If $G$ is an undirected and connected graph with minimum degree $k$, then $\lambda\left(G\right)>k$.
It is impossible to have a planar graph with ten vertices whose number of regions is twice the number of its edges.
The value of $\chi'\left(K_5\right)$ - the edge-chromatic number of $K_5$ - is five. (Remember that $K_5$ is the complete graph with five vertices.)
If $G$ is the following graph, then what is the value of $\kappa\left(G\right)$?
1
2
3
4
What is the value of $\lambda\left(G\right)$ for the graph $G$ in the previous question?
1
2
3
4
Which of the following statements is TRUE?
A bipartite graph does not contain any cycle.
The value of $\chi'\left(K_4\right)$ - the edge-chromatic number of the complete graph with four vertices - is 4.
Let $G$ be a simple, undirected and connected graph. The Menger's theorem states that: the value of $\kappa\left(G\right)$ is the maximum number of vertex-independent paths in $G$ between two arbitrary vertices $u$ and $v$ with $u \ne v$.
The edges of every undirected graph $G$ can be colored with either $\Delta\left(G\right)$ or $\Delta\left(G\right)+1$ colors such that every two edges that share a vertex will get different colors. (Here $\Delta\left(G\right)$ denotes the maximum degree in $G$.)
