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
A principal node is a
Which of the following statement(s) is/are correct regarding about the undirected graph?
I. Number of odd degree vertices is even.
II. Sum of degrees of all vertices is even.
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?
- Let $G$ be an edge-weighted undirected graph with positive edge weights. Suppose a positive constant $\alpha$ is added to the weight of every edge.
Which ONE of the following statements is TRUE about the minimum spanning trees (MSTs) and shortest paths (SPs) in $G$ before and after the edge weight update? - Maintaining a graph in memory by means of its adjacency matrix is known as
