3 votes 3 votes For which values of m and n is Km,n regular? Graph Theory graph-theory + – sourav. asked Aug 10, 2016 sourav. 2.0k views answer comment Share Follow See all 9 Comments See all 9 9 Comments reply Prashant. commented Aug 10, 2016 reply Follow Share sourav km,n(complete graph) is always regular for m=n 0 votes 0 votes srestha commented Aug 10, 2016 reply Follow Share Km,n is complete bipartite graph. It is regular too As we can say complete graph is a subset of regular graph 0 votes 0 votes sourav. commented Aug 10, 2016 reply Follow Share its asking about complete bipartite graph.what should be the value of m,n to make complete bipartite graph a regular graph. according to me it should be m=n=n/2....just want to verify 0 votes 0 votes srestha commented Aug 10, 2016 reply Follow Share complete bipartite graph $\subset$ complete graph $\subset$ regular graph So, put any value in m,n 0 votes 0 votes sourav. commented Aug 10, 2016 reply Follow Share A regular graph is a graph in which all the vertices have same degree....yes obviously complete graph is (n-1)regular graph. here in the question it is given Km,n i.e it is a complete bipartite graph but it is not true that for ny value of m,n it will be a regular bipartite graph...let us take K2,3 ..i.e m=2 and n=3 now it will be degree having 3,3,2,2,2. If we take k 2,2 (m=n)now the degree will be 2,2,2,2 0 votes 0 votes srestha commented Aug 10, 2016 reply Follow Share Ok I think bipartite graph like something different to think yes $K_{2}$ is isomorphic to $K_{2,2}$ but is $K_{3}$ is isomorphic to $K_{3,3}$ ? No $K_{3}$ is planer where $K_{3,3}$ is non planer Similarly $K_{2,3}$ has 2 partition in the graph and each partition has regular by itself 0 votes 0 votes sourav. commented Aug 10, 2016 reply Follow Share not as a whole it is not regular ...!!!! if you are asked to write the degree sequence of K2,3 then it will be 3,3,3,2,2 but has to be n,n,n,n,n for Kn,m where n=m; 0 votes 0 votes srestha commented Aug 10, 2016 reply Follow Share Is complete bipartite graph is complete graph? What will be ur answer? definitely No but it is complete as a bipartite graph. Similarly as it is regular bipartite graph , as a whole No bipartite graph could be regular. . Do, u think $K_{3,3}$ is a regular graph? No . 0 votes 0 votes sourav. commented Aug 10, 2016 reply Follow Share Yes ,a complete bipartite graph can be regular graph K m,n provided m=n reference (exmpl 3) https://www.cs.cmu.edu/~adamchik/21-127/lectures/graphs_5_print.pdf 1 votes 1 votes Please log in or register to add a comment.