Question

Create a graph with 4 vertices of degrees 2, 2, 3, 3 or explain why no such graph exists. If the graph exists, draw the graph, label the vertices and edges. To answer the question in the box below, write the vertex set, the edge set, and the edge-endpoint function as shown on page 627 of the text. You can copy (Ctrl-C) and paste(Ctrl-V) the table to use in your answer if you like. Vertex set- Edge set Edge-endpoint function: Edge Endpoints

Discrete Math

Answer 1

CL Gbe a graph on n vertices and le リda , ds, dn are degrees of n-vertices Then increasing ar decreasing scquenee kdn s colled degree sequence of The given degree sequence is grephical if exe esist ygraph with given degree sequente simple To determine given legrce sequence is graphica ox not De use HavelHakimi theorerm decreaging ience is grophical İff.-竹e modi ed.sequen 1 C

For example, consider the sequsence frst no 13 3 3 2 fom selected Arange no,s, n dereaung Seleet neset tos no As ive get al zerv Sequendels graphical and the graeh Such olugrees exist -with oligrees exist guch 어

No uo consicer gen p plem. toe toant graph oith 4 vahices uwith degree's 2, 2, 3,3 we check is it grephical sea onte i decreaging order cuts and subtra 다 4froro selected n o .s Skep ) Seleet meet tso no,s cut 2 and Subha fyonn selected no s - A1 zers. Sequence is qraphicl Hence Such groph exist uwith sour verhices and degrees 2 ,2, 3,3

Let we draia graph consider four verticesA B, C,D plot fnur verticesA LB vertex set-tA,B,c,Dと Edge .sdal_t AB, Ac,AD, BC.BDE soo step I we sele ded vetices e, c,D so dai one edge fom A to B, A tp and A tod simillary ten stp r) we seledted vertices c and p the above graph is required graph.. oith tour verbices and degsees 2,2, 3, 3