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What is an adjacency matrix?
An adjacency matrix is a matrix showing which vertices of a graph are adjacent to which other vertices.
Write adjacency and incidence matrix for all the graphs developed?
adjacency matrix- since the edges are the relationship between two vertices ,the graph can be represented by a matrix,
What is the definition of a symmetric matrix?
Symmetric Matrix:Given a square matrix A such that A'=A, where A' is the transpose of A, then A is a symmetric matrix.note: No need to think about diagonal elements, they can be anything.
Is null square matrix a skew symmetric?
yes, it is both symmetric as well as skew symmetric
An adjacency matrix representation of a graph cannot contain information of?
parallel edges
Find directed graph that has the adjacency matrix?
Find directed graph that has the adjacency matrix Find directed graph that has the adjacency matrix
What is an adjacency matrix?
An adjacency matrix is a matrix showing which vertices of a graph are adjacent to which other vertices.
Write adjacency and incidence matrix for all the graphs developed?
adjacency matrix- since the edges are the relationship between two vertices ,the graph can be represented by a matrix,
When should one use an adjacency matrix instead of an adjacency list in graph representation?
An adjacency matrix is more suitable for representing dense graphs with many edges, while an adjacency list is better for sparse graphs with fewer edges. Use an adjacency matrix when the graph is dense and you need to quickly check for the presence of an edge between any two vertices.
Prove that a matrix which is both symmetric as well as skew symmetric is a null matrix?
Let A be a matrix which is both symmetric and skew symmetric. so AT=A and AT= -A so A =- A that implies 2A =zero matrix that implies A is a zero matrix
What is a skew symmetric matrix?
A skew symmetric matrix is a square matrix which satisfy, Aij=-Aji or A=-At
What are the differences between an adjacency matrix and an adjacency list in terms of representing graph data structures?
An adjacency matrix is a 2D array that represents connections between nodes in a graph, with each cell indicating if there is an edge between two nodes. An adjacency list is a collection of linked lists or arrays that stores the neighbors of each node. The main difference is that an adjacency matrix is more space-efficient for dense graphs, while an adjacency list is more efficient for sparse graphs.
What is the definition of a symmetric matrix?
Symmetric Matrix:Given a square matrix A such that A'=A, where A' is the transpose of A, then A is a symmetric matrix.note: No need to think about diagonal elements, they can be anything.
What is the eigen value of a real symmetric matrix?
The eigen values of a real symmetric matrix are all real.
What is a symmetric matrix?
a square matrix that is equal to its transpose
What are the differences between adjacency list and adjacency matrix in graph theory?
In graph theory, an adjacency list is a data structure that represents connections between vertices by storing a list of neighbors for each vertex. An adjacency matrix, on the other hand, is a 2D array that indicates whether there is an edge between two vertices. The main difference is that adjacency lists are more memory-efficient for sparse graphs, while adjacency matrices are better for dense graphs.
Is null square matrix a skew symmetric?
yes, it is both symmetric as well as skew symmetric
