Question

1: EDGES OF THE BIPARTITE GRAPH Please select file(s) Select image(s) 2: 3-regular graphs 2.1: FOR WHAT N IS THERE A SIMPLE 3-REGULAR GRAPH WITH N VERTICES? Please select file(s) Select image(s) 2.2 Please select file(s) Select image(s) 2.3 Please select file(s) Select image(s) 3:2-regular and 3-regular graphs 3.1: EVERY TWO CONNECTED 2-REGULAR GRAPHS WITH THE SAME NUMBER OF VERTICES ARE ISOMORPHIC. Please select file(s) Select image(s) 3.2: TWO CONNECTED, SIMPLE, 3-REGULAR GRAPHS WITH 8 VERTICES. Please select file(s) Select image(s)

Answer 1

1 we consider à complete bipartite graph K22 13 Here vertices are V,,V2, 3, and edges are V, V3, V. Nu, V2 V3, V2 V4.

2 For , N = 4, Simple Lad,' и 3-regular yark 3-аr graph a vertices is 2.2 for N=6 Simple 3-regular uple 3-regular graph graph with 5 vertices is For n=8 Simple 3-regular graph with 8 vertica For N is even a simple 3-regular graph with Nertices has degree sum 3N, which is even. Then this is possible But for N is odd N vertices has degree a simple 3-regular graph with sum 3N, which is odd which is not possible [' the graph is 3-regular I and Id(i) = 2161 ViEV 1

we lake two 2-regular graph G and G. with 4 vertices at then both are isomorphie Since a b 3.2 63 G and Gz are 3-regular simple graph with 8 vertices