21. Use paths either to show that these graphs are not isomor- phic or to find an isomorphism between them. 18 U6 G 12 U5 13 UA V8 V7' V6 H V2 V5 V3 VA

Write a java program for dominant set of vertices, graph and at least one adjance vertex of set s.

Code in Python Please For an undirected graph G with n vertices, prove the following are equivalent: G is a tree G is connected, but if any edge is removed the resulting graph is not connected. For any two distinct vertices , u and v , there is exactly one simple path from u to v. G contains no cycles and has n-1 edges

Plz do all a, b, c

H.w: show that Let x be a e dge of Connected graph G. The following statements are equivalent. (1) X is X is a bridge of G (2) X is not on any eycle of G ® There exist vertices u and vof G such the ecdgex is on every path goning u and V O There exists a pardition of V into su bsets ų and w such that for any verticesUEU and w the edge x ison every path joining u and w

Construct all regular graphs that exist for the vertex set V = {1, 2, 3, 4}. For example, G = (V,E0) where E0 = {} is one possible graph

req code in java

vdv

Select the graph that is not regular. в D B D D C A B

Write a program for depth-first traversal on the following graph using the algo-rithm defined in this week