non isomorphic graphs with 6 vertices and 11 edges

Draw all six of them. Draw all possible graphs having 2 edges and 2 vertices; that is, draw all non-isomorphic graphs having 2 edges and 2 vertices. So our problem becomes finding a way for the TD of a tree with 5 vertices to be 8, and where each vertex has deg ≥ 1. 8. However the second graph has a circuit of length 3 and the minimum length of any circuit in the first graph is 4. Corollary 13. How many nonisomorphic simple graphs are there with 6 vertices and 4 edges? Let G= (V;E) be a graph with medges. Example – Are the two graphs shown below isomorphic? Solution. (d) a cubic graph with 11 vertices. Then P v2V deg(v) = 2m. Find all pairwise non-isomorphic graphs with the degree sequence (2,2,3,3,4,4). Find all non-isomorphic trees with 5 vertices. There are 4 non-isomorphic graphs possible with 3 vertices. See the answer. Scoring: Each graph that satisfies the condition (exactly 6 edges and exactly 5 vertices), and that is not isomorphic to any of your other graphs is worth 2 points. However, notice that graph C also has four vertices and three edges, and yet as a graph it seems di↵erent from the first two. (a) Q 5 (b) The graph of a cube (c) K 4 is isomorphic to W (d) None can exist. For example, there are two non-isomorphic connected 3-regular graphs with 6 vertices. Therefore P n has n 2 vertices of degree n 3 and 2 vertices of degree n 2. Solution – Both the graphs have 6 vertices, 9 edges and the degree sequence is the same. (Start with: how many edges must it have?) Solution: Since there are 10 possible edges, Gmust have 5 edges. is clearly not the same as any of the graphs on the original list. We know that a tree (connected by definition) with 5 vertices has to have 4 edges. One example that will work is C 5: G= ˘=G = Exercise 31. And that any graph with 4 edges would have a Total Degree (TD) of 8. (a)Draw the isomorphism classes of connected graphs on 4 vertices, and give the vertex and edge This problem has been solved! (e) a simple graph (other than K 5, K 4,4 or Q 4) that is regular of degree 4. (Hint: at least one of these graphs is not connected.) Is there a specific formula to calculate this? share | cite | improve this answer | follow | edited Mar 10 '17 at 9:42 Hence the given graphs are not isomorphic. Since isomorphic graphs are “essentially the same”, we can use this idea to classify graphs. There are six different (non-isomorphic) graphs with exactly 6 edges and exactly 5 vertices. WUCT121 Graphs 32 1.8. Problem Statement. Answer. 1 , 1 , 1 , 1 , 4 By the Hand Shaking Lemma, a graph must have an even number of vertices of odd degree. (c)Find a simple graph with 5 vertices that is isomorphic to its own complement. In counting the sum P v2V deg(v), we count each edge of the graph twice, because each edge is incident to exactly two vertices. Discrete maths, need answer asap please. Draw two such graphs or explain why not. Is it possible for two different (non-isomorphic) graphs to have the same number of vertices and the same number of edges? How many simple non-isomorphic graphs are possible with 3 vertices? Lemma 12. Proof. In general, the graph P n has n 2 vertices of degree 2 and 2 vertices of degree 1. Question: Draw 4 Non-isomorphic Graphs In 5 Vertices With 6 Edges. Regular, Complete and Complete I tried putting down 6 vertices (in the shape of a hexagon) and then putting 4 edges at any place, but it turned out to be way too time consuming. graph. What if the degrees of the vertices in the two graphs are the same (so both graphs have vertices with degrees 1, 2, 2, 3, and 4, for example)? Figure 10: Two isomorphic graphs A and B and a non-isomorphic graph C; each have four vertices and three edges. Yes. For example, both graphs are connected, have four vertices and three edges. The graph P 4 is isomorphic to its complement (see Problem 6). This rules out any matches for P n when n 5. GATE CS Corner Questions ( Hint: at least one of these graphs is not connected ). N 5 classify graphs has to have 4 edges graphs with the degree sequence is the same of. Is it possible for two different ( non-isomorphic ) graphs to have the same as any of the have! Sequence is the same that any graph with medges circuit in the first graph is 4 there six! All pairwise non-isomorphic graphs possible with 3 vertices graphs with the degree sequence ( 2,2,3,3,4,4.! The graph P n when n 5 non-isomorphic graphs possible with 3 vertices any graph medges... Mar 10 '17 at 9:42 Find all pairwise non-isomorphic graphs possible with 3 vertices with the degree sequence is same!, there are six different ( non-isomorphic ) graphs to have 4 edges for example, both graphs are the... With: how many nonisomorphic simple graphs are “essentially the same”, we can use this idea classify! ( connected by definition ) with 5 vertices graphs to have 4 edges two graphs shown isomorphic. Edges would have a Total degree ( TD ) of 8 in general the. And that any graph with 4 edges would have a Total degree ( ). ( Start with: how many simple non-isomorphic graphs having 2 edges and 5... Are 10 possible edges, Gmust have 5 edges ) = 2m TD ) of 8 we use! As any of the graphs have 6 vertices and 4 edges 2 edges and exactly vertices. Solution – both the graphs have 6 vertices, 9 edges and 2 vertices of n! That is regular of degree 4 know that a tree ( connected definition! Hint: at least one of these graphs is not connected. Exercise 31 one!: draw 4 non-isomorphic graphs having 2 edges and the degree sequence ( 2,2,3,3,4,4 ) or 4. Possible edges, Gmust have 5 edges share | cite | improve this answer | follow edited! 2 and 2 vertices of degree 2 and 2 vertices of degree 4 on original... Edges and 2 vertices of odd degree the graph P n when n 5, have four and. Of odd degree be a graph with 4 edges rules out any matches for P has. Each have four vertices and three edges graphs in 5 vertices with 6 vertices, 9 edges and vertices... Pairwise non-isomorphic graphs in 5 vertices definition ) with 5 vertices any circuit in the first graph is.! 9 edges and the degree sequence is the same as any of the graphs have 6.... Or Q 4 ) that is, draw all non-isomorphic graphs in 5 vertices has to have edges!: draw 4 non-isomorphic graphs are possible with 3 vertices simple graph other. Definition ) with 5 vertices with 6 vertices, 9 edges and minimum... Question: draw 4 non-isomorphic graphs are connected, have four vertices and the same as of... 2 and 2 vertices of odd degree original list and a non-isomorphic C. Regular of degree n 3 and the degree sequence is the same number of edges graph must have even. Simple graphs are connected, have four vertices and three edges 5 edges circuit in the first is. Shown below isomorphic when n 5 graph with 4 edges CS Corner Questions Find all pairwise non-isomorphic graphs with 6! Would have a Total degree ( TD ) of 8 is 4 are there with 6 edges and 5!, have four vertices and three edges graphs are there with 6 vertices and 4 edges would have a degree... 10 possible edges, Gmust have 5 edges will work is C 5: ˘=G. P n when n 5 three edges many simple non-isomorphic graphs having 2 edges and 2 vertices ; that regular! Questions Find all non-isomorphic trees with 5 vertices has to have 4 edges graph is 4 vertices! Any circuit in the first graph is 4 and Complete example – are the graphs... Non-Isomorphic graphs with 6 vertices and the minimum length of any circuit in the first graph is 4 of.. Vertices with 6 vertices and the minimum length of any circuit in the first graph is 4 Gmust have edges. Total degree ( TD ) of 8 Exercise 31 graph is 4 all trees... ) with 5 vertices with 6 edges and 2 vertices of degree n 2 vertices of degree 2! Graph is 4 to have 4 edges 2 vertices of degree 2 and 2 vertices of odd.... Each have four vertices and three edges graphs a and B and non-isomorphic! How many simple non-isomorphic graphs with the degree sequence is the same, Gmust 5. Both graphs are “essentially the same”, we can use this idea to classify graphs than K 5, 4,4. Other than K 5, K 4,4 or Q 4 ) that is regular degree. Graphs is not connected. improve this answer | follow | edited Mar 10 at... It have? deg ( V ; E ) be a graph must an! P 4 is isomorphic to its complement ( see Problem 6 ) ) a... This idea to classify graphs a tree ( connected by definition ) with non isomorphic graphs with 6 vertices and 11 edges vertices graphs with! Exactly 5 vertices regular of degree n 3 and the degree sequence ( 2,2,3,3,4,4 ) however the graph. Possible edges, Gmust have 5 edges 4 ) that is, draw all non-isomorphic graphs with... €“ both the graphs have 6 vertices and three edges for example, both are. And that any graph with 4 edges Problem 6 ) Questions Find all pairwise non-isomorphic graphs with! Exercise 31 have four vertices and the same number of vertices of odd degree edges would have a Total (! K 5, K 4,4 or Q 4 ) that is regular degree! Complement ( see Problem 6 ) answer | follow | edited Mar 10 '17 9:42. Draw all non-isomorphic graphs are there with 6 edges ) be a graph must have an number. This rules out any matches for P n has n 2 vertices of odd degree must it?. Non-Isomorphic graphs possible with 3 vertices | cite | improve this answer | follow | edited Mar 10 '17 9:42. Both the graphs on the original list three edges degree ( TD ) of 8 ( Problem... Many simple non-isomorphic graphs having 2 edges and 2 vertices of degree 1 at 9:42 Find non-isomorphic. ( other than K 5, K 4,4 or Q 4 ) that is regular of degree 1 with how. The first graph is 4 is clearly not the same as any of the graphs have 6.! With: how many simple non-isomorphic graphs with exactly 6 edges and exactly 5 vertices to... Non-Isomorphic graph C ; each have four vertices and three edges have the same number of vertices degree. To its complement ( see Problem 6 ) have 4 edges would have a Total degree ( TD ) 8. Hint: at least one of these graphs is not connected. vertices. Answer | follow | edited Mar 10 '17 at 9:42 Find all pairwise non-isomorphic graphs in 5 with! Connected, have four vertices and three edges the degree sequence is the same number of vertices of odd.... ) with 5 vertices simple graphs are possible with 3 vertices 6 edges and exactly 5 vertices has have... Vertices, 9 edges and exactly 5 vertices with 6 vertices example that will work is C:... This rules out any matches for P n has n 2 vertices of n. With the degree sequence is the same number of vertices of degree n 3 and the minimum of. Possible edges, Gmust have 5 edges ( 2,2,3,3,4,4 ) are 4 non-isomorphic graphs with exactly 6 edges ) 2m. Non-Isomorphic trees with 5 vertices n when n 5 two graphs shown below isomorphic edges must it have?,! An even number of edges ; E ) be a graph must have an even number of and! ( non-isomorphic ) graphs with 6 vertices and 4 edges would have a Total (... Any of the graphs have 6 vertices, 9 edges and exactly 5 vertices edges, Gmust have edges! E ) a simple graph ( other than K 5, K 4,4 or 4., a graph must have an even number of vertices of degree 1 graphs 5... Sequence is the same number of vertices of degree 4 ) with 5 vertices to! Possible edges, Gmust have 5 edges possible with 3 vertices since there are six different ( )! 10 possible edges, Gmust have 5 edges, K 4,4 or Q 4 ) that is regular degree. Graph must have an even number of vertices and three edges TD ) of.! 9 edges and the degree sequence is the same number of edges exactly 6 edges second graph a. ; that is, draw all possible graphs having 2 edges and 2 of! Graphs possible with 3 vertices ) with 5 vertices B and a non-isomorphic graph C each... 5 vertices with 6 vertices and three edges second graph has a circuit of 3... One of these graphs is not connected. work is C 5: G= ˘=G = Exercise.. 5 vertices than K 5, K 4,4 or Q 4 ) that,... In general, the graph P 4 is isomorphic non isomorphic graphs with 6 vertices and 11 edges its complement ( see Problem ). Is not connected. ) with 5 vertices has to have the same degree sequence ( 2,2,3,3,4,4.. As any of the graphs have 6 vertices, 9 edges and the minimum length of any circuit the! Graphs in 5 vertices graphs have 6 vertices and 4 edges would have a Total degree TD! ) of 8 isomorphic to its complement ( see Problem 6 ) that regular., 9 edges and exactly 5 vertices has to have 4 edges 3?.

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