4 votes 4 votes Let $\text{K}(4,6)$ be the complete bipartite graph on $10$ vertices, having $4$ vertices in one part and having $6$ vertices in another part. Which of the following is/are true? Number of edges in the complement of $\text{K}(4,6)$ is $21.$ The number of connected components in the complement of $\text{K}(4,6)$ is $1.$ Each connected component in the complement of $\text{K}(4,6)$ is a complete graph. Either $\text{K}(m,n)$ OR complement of $\text{K}(m,n)$ is dis-connected. Graph Theory goclasses2024-dm-5-weekly-quiz goclasses graph-theory graph-connectivity multiple-selects 2-marks + – GO Classes asked May 11, 2022 • edited May 27, 2023 by Lakshman Bhaiya GO Classes 375 views answer comment Share Follow See all 0 reply Please log in or register to add a comment.
4 votes 4 votes Each connected component in complement of $\text{K}(m,n)$ is a complete graph, one is $\text{K}_{m},$ another is $\text{K}_{n}.$ So, total number of edges in complement of $\text{K}(m,n)$ is $n(n-1)/2 + m(m-1)/2$ So, A;C;D is correct. GO Classes answered May 11, 2022 GO Classes comment Share Follow See all 2 Comments See all 2 2 Comments reply ankush8523 commented Nov 13, 2022 reply Follow Share complement of K(m,n) is always disconnected and K(m,n) is always connected so why d is correct 1 votes 1 votes GovindYadav29 commented Dec 1, 2022 reply Follow Share @ankush8523 Because Option D is saying anyone of the K(m,n) OR its complement is disconnected. (FOCUS – on the word “OR”) As we know that comlement of K(m,n) is disconnected. So the option D holds the truth. 1 votes 1 votes Please log in or register to add a comment.