2 votes 2 votes Graph Theory graph-theory + – Pinku Kumar Jha asked Jun 13, 2016 • retagged Oct 11, 2023 by Hira Thakur Pinku Kumar Jha 13.5k views answer comment Share Follow See all 2 Comments See all 2 2 Comments reply vijaycs commented Jun 13, 2016 reply Follow Share Not able to see your graph bro ... R u ?? 0 votes 0 votes Pinku Kumar Jha commented Jun 13, 2016 reply Follow Share bro..i used general notation for any graph...k->complete graph,c->cyclic graph ,w->wheel graph,Q->hypercube,and n for their dimensions...as given in rosen chapter 10.2 ,Q.no-35 0 votes 0 votes Please log in or register to add a comment.
2 votes 2 votes Complete graph Kn = nC2 edges Cycle graph Cn = n edges Wheel graph Wn= 2n edges Bipartite graph Km,n = mn edges Hypercube graph Qn = 2n-1⨉n edges srestha answered Jun 13, 2016 srestha comment Share Follow See all 16 Comments See all 16 16 Comments reply Pinku Kumar Jha commented Jun 14, 2016 reply Follow Share @srestha ..can u tell me? how should i approach for calculating no of edges in hypercube.. 0 votes 0 votes srestha commented Jun 14, 2016 reply Follow Share it is a formula say hypercube has 3 bits then Q3 =22 *3=12 0 votes 0 votes Sushant Gokhale commented Sep 16, 2016 reply Follow Share @Sreshtha. For Kn, we mean the graph is 'K' regular i.e. every vertex has degree 'K'. So, sum of degrees of all vertices= nK We have counted every edge twice. So, total edges = nk/2. –1 votes –1 votes Sushant Gokhale commented Sep 16, 2016 reply Follow Share Sorry Sreshtha. Kn is (n-1) regular graph. So, your answer is right. 0 votes 0 votes Sushant Gokhale commented Sep 16, 2016 reply Follow Share @SReshtha. Wn = 2(n − 1) (From wiki) 1 votes 1 votes srestha commented Sep 16, 2016 reply Follow Share Prove it with a figure 0 votes 0 votes Sushant Gokhale commented Sep 16, 2016 reply Follow Share @Sreshtha. Consider W4. W4 = C3 + (add one vertex and connect it to all the vertices)....................general formula = (3 edges) + (edge per vertex connected i.e. 3 edges) =2 (3) = 2(n-1) 1 votes 1 votes srestha commented Sep 16, 2016 reply Follow Share No that is not a wheel graph chk for wheel graph 0 votes 0 votes Sushant Gokhale commented Sep 17, 2016 reply Follow Share https://en.wikipedia.org/wiki/Wheel_graph 0 votes 0 votes Akriti sood commented Dec 9, 2016 reply Follow Share @srestha,in bipartite graph how can you say that number of edged are n*m in complete bipartite graph,the number of edges are n*m as there each vertex of first partition forms edge with each vertex of second partition. but how can you say about a bipartite graph which is not complete. 0 votes 0 votes srestha commented Dec 9, 2016 reply Follow Share @Akriti take an example , u will get it 0 votes 0 votes Akriti sood commented Dec 9, 2016 reply Follow Share oh i am sorry..i forgot Km.n means complete bipartite.Thanks 0 votes 0 votes reena_kandari commented Aug 7, 2017 i edited by reena_kandari Aug 7, 2017 reply Follow Share @Srestha. for wheel graph wiki has different definition from the ROSEN. according to rosen: We obtain a wheel Wn when we add an additional vertex to a cycle Cn, for n ≥ 3, and connect this new vertex to each of the n vertices in Cn, but according to wiki a wheel Wn when we add an additional vertex to a cycle Cn-1, and connect this new vertex to each of the n vertices in Cn, by new edges everywhere in the internet has different definition from ROSEN. 0 votes 0 votes srestha commented Aug 8, 2017 reply Follow Share @reena donot worry, such an easy question iit professor will not choose :p 0 votes 0 votes reena_kandari commented Aug 8, 2017 reply Follow Share yeah, but we must know it na.they may ask in some other sense where wheel graph may needed then we have decide which definition to follow. 0 votes 0 votes srestha commented Aug 8, 2017 reply Follow Share yes, wiki one is more correct. just understand the concept, that is enough 0 votes 0 votes Please log in or register to add a comment.