Calculating Rooted Trees in Phylogeny for Three Species
The number of possible distinct rooted phylogenetic trees for a given number of species can be determined using a specific formula related to bifurcating trees.
Formula for Rooted Trees
For '$n$' species (or taxa), the number of distinct rooted tree topologies is calculated using the double factorial notation: $N = (2n - 3)!!$ where '$n$' is the number of species.
Applying the Formula
In this case, we have three species, so $n = 3$. We substitute this value into the formula:
- Number of trees = $(2 \times 3 - 3)!!$
- Simplify the expression inside the factorial: $(6 - 3)!! = 3!!$
- Calculate the double factorial: $3!! = 3 \times 1 = 3$.
Conclusion
Therefore, there are 3 distinct possible rooted trees for a phylogeny involving three species.
Important Questions from Graph Theory
Let $G(V, E)$ be an undirected and unweighted graph with 100 vertices. Let $d(u, v)$ denote the number of edges in a shortest path between vertices $u$ and $v$ in $V$. Let the maximum value of $d(u, v)$, $u, v \in V$ such that $u \neq v$, be 30. Let T be any breadth-first-search tree of G. Which ONE of the given options is CORRECT for every such graph G?
- Maintaining a graph in memory by means of its adjacency matrix is known as
Let G be a simple undirected planar graph on 10 vertices with 15 edges. If G is a connected graph, then the number of bounded faces in any embedding of G on plane is equal to_________.
Consider the following statements regarding graph theory :
1. Chord is that branch of the graph that does not belong to the particular tree.
2. Cut-set is a unique set with respect to a given tree of a connected graph containing one chord and all of the free branches contained in the free path formed between two vertices of the chord.
3. If M represents the number of branches and N the number of nodes, the minimum number of variables involved in analyzing a network is equal to $(M + N − 1)$.
Which of the above statements are not correct?
The incidence matrix of the graph shown
