2 votes 2 votes Let $A$ be a $3 \times 6$ matrix with real-valued entries. Matrix $A$ has rank $3$. We construct a graph with $6$ vertices where each vertex represents distinct column in $A$, and there is an edge between two vertices if the two columns represented by the vertices are linearly independent. Which of the following statements $\text{MUST}$ be true of the graph constructed? Each vertex has degree at most $2$. The graph is connected. There is a clique of size $3$. The graph has a cycle of length $4$. The graph is $3$-colourable. Graph Theory tifr2021 graph-theory graph-coloring matrix + – soujanyareddy13 asked Mar 25, 2021 • recategorized Nov 20, 2022 by Lakshman Bhaiya soujanyareddy13 605 views answer comment Share Follow See 1 comment See all 1 1 comment reply anirudhkumar18 commented Oct 23, 2023 reply Follow Share @Deepak Poonia sir, Rank of matrix is 3 so #Linear independent column. hence we got clique of size 3. but each vexterx has degree atmost 2 seems it is correct option. 0 votes 0 votes Please log in or register to add a comment.
0 votes 0 votes Option C) There is a clique of size 3. rank of matrix A is 3, Therefore 3 of the columns must be linearly independent of each other, Hence a clique of size 3. Nikhil_dhama answered Apr 4, 2021 Nikhil_dhama comment Share Follow See all 2 Comments See all 2 2 Comments reply Aaru_2023 commented Dec 29, 2022 reply Follow Share @Deepak Poonia the graph im getting is $K_{3}$ along with 3 isolated vertex, here clique of size $3$ is present but im getting option $E$ also that it is 3 colourable. 0 votes 0 votes nayan_dubey commented Jun 7, 2023 reply Follow Share @Deepak Poonia could you explain this question 0 votes 0 votes Please log in or register to add a comment.