Which graph is Eulerian? Which graph is not Eulerian but contains anEulerian path?Graph -Graph 2Graph 3

Answered: Which graph is Eulerian? Which graph is…

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 1CT

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(b) Graph H is the complete simple graph with 17 vertices, K17. What kind of circuits does G have? ✓ [Select] H has a Hamiltonian circuit but no Euler circuit H has an Euler circuit but no Hamiltonian circuit H has both an Euler circuit and a Hamiltonian circuit It is not possible to tell which kind (s) of circuits H has from this information , the resulting subgraph
How do we know the graph K, has an Euler path using the Euler Theorem?
Prove Forward and Reverse: A connected undirected graph has a Eulerian Path iff it has 2 vertices of odd degree
6© Conaider a gaaph with 11 Vertices, which has at what will lbe X(4). 'Color this graph (Show all staps) least one yeleor clique abo. Suppose thire find menimum bipantite metching en that 6 people and 6 tesks are Penson is Tasks TI, T6 asaijned to I4 73, T6 T2, T3, TS T4, Tb E TI, T2, T4 .
Sletch the Grapn Graph Of y= 3seccax)
Is it possible for a graph with 6 vertices to have degrees 2, 2, 2, 3, 5, and 9? (Loops are allowed.) Yes or No?
Find the chromatoc number x and the edge-chromatic number x' for this graph. Also clecide whether it has å Hami Honian oycle andlor an fuler cırcuit. If it does not hQue an Eulen circult, does it have an Eulen path? (a) (6)
Ouestion 2 (a) Show that the Petersen graph is nonplanar. [Hint: show that the graph is edge contractible to Ks). (b) Write down two induced subgraphs of the Petersen graph. (c) Show that the simple connected planar graph with 17 edges and 10 vertices cannot be properly coloured with two colours. [Hint: Show that such a graph must contain a triangle. Prove by contradiction]. (d) Suppose G is a connected, simple finite planar graphs with n > k vertices. Show that G has at most (n - 2) edges. (e) Let G be a connected planar graph with 20 vertices each of degree 3. Find the number of regions in the graph. (f) Prove that a planar graph with n 2 4 vertices in which every vertex has degree at least 2 has at least 4 vertices.
Exercise #3," Which graph is Eulerian? Which graph is not Eulerian but contains an Eulerian path? 区>> Graph 1 Graph 2 Graph 3

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Which graph is Eulerian? Which graph is not Eulerian but contain ai Eulerian path? Graph - Graph 2 Graph 3