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List Roprescrilahon Of; undclisctid Goeaph— tod Implementation of a Crraph— =) ao are useighka Graph — dlobeno max 30 gees Struct neele an worl § Shuck neck Hrnoxt 5 4h mec 15 meds{ *adfLmax]'5 3 Por_weighld Gaph — “gece Shc ned “- water '5 ite weeight' Stich neodle ¥ next 5 % nede 1, meds L jad imax, 1. Weighted Graph : A graph is said to be a weighted graph if all the edger in it are labelled with some numbers. It is shown in the Fig. 12.4 below. Fig. 12.4, 2, Self Loop : Ifthere is an edge whose starting and end ele are ae that s (Ua U9) isan edge then it is called a self loop or simply a loop. It is s on " im an vert 3. Parallel Edges : If there are more than one edge between the s vertices then they are known as parallel edges. yier 10. ii. 12. 13. 14. 15. 16. V7. 18, 19, Regular graph : A graph is regular if og. game number of nodes. every node is adjacent to the Q) Here every node is adjacent to 3 nodes. 7? Planer graph : A graph is planar if it can be : . any two edges intersecting. drawn in a plane without LN Connected graph : In a graph G, two vertices v (3) 4) . : 7 , and v, ar i 7 connected if there is a path in G from v, to v, or » to v,. Aerorhiss a R raion to be connected if there is a path from any node of orenh ‘oie sal ‘egular graph node, i.e., for every pair of distinct vertices in G, there is a ath other ®@ (a) Connected graph (b) Not connected graph Fig. 12.10. (a) Strongly Connected Graph : A directed graph is said to be strongly connected graph if for every pair of distinct vertices in G, there is a path. (vb) Weakly Connected Graph : A diagram is called weakly connected or unilaterally connected if for any pair of nodes u and v, there is a path from u to v or a path from v to u. If from the diagraph we Fig. 12.11. remove the directions and the resulting undirected graph is connected then that diagraph is weakly connected. Figure 12.11 shows a weakly connected graph. Cycle : If there is a path containing one or more edges which starts from a vertex and terminates into the same vertex then the path is called as a cycle. Acyclic graph: Ifa graph (digraph) does not have any cycle then it is called as acyclic graph. Cyclic graph : A graph that has cycles is called a cyclic graph. n(n-1) Maximum edges in graph: Inan undirected graph there can be —_ maximum edges and in a directed graph there can be n(n — 1) maximum edges. Where n is the total number of vertices in the graph. b Articulation point : If on removing a node from the graph, the graph becomes disconnected then that node is called the articulation point. Bridge : If on removing an edge from the graph, the graph becomes disconnected then that edge is called the bridge . eee F ch. Biconnected graph: A graph with no articulation points is calleda biconnected grap == Diference between cycle and Hamiltonian cycle Cycle is a closed walk through the graph with repeated vertices having the same starting and ending vertex called a cycle. Hamiltonian cycle is also a cycle having a closed walk through the graph but the vertices in the cycle are not repeated at all. In other words a cycle having all the vertices with same starting and ending vertex in which every vertex appears only once. For example - Consider Graph G. Hamiltonian cycle is A-B-D-E-C-F-A. -y Ay BDL 5 A,sw HL 4c — A,BWOF,CLF Abs. if nt BFS Hough Quarg _— Z unseat Elomont- An07 ths bie ama al @ Dds re sutee netplbetrs anil ¥ ss “as © ti Luce 8¢ chem . O eepeat Sep] wnlile Ihe qyeave SOME A exe— £ a Cc D \woahe 0 Adyaw lst a A5D p DE C D D £ - mi | {Tj Rear Peto freak “eo An Peo “Toued nade = A trem Te Fraursed =medes=Ary 350 See ® Ageun de Porass u's eneposte prec Frenl? 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