Boesch, F., Tindell, R.: Connectivity and symmetry in graphs. In: Graphs and applications (Boulder, Colo., 1982). Wiley-Intersci. Publ. Wiley, New York (1985) 53--67  Home/Search   Document Not in Database   Summary   Related Articles   Check

....for cycles, crowns, chordal rings and n ary 2cubes. These graphs are highly symmetric and attractive for communication networks due to their regularity, symmetry, and small diameter. The connectivity and reliability of this class of graphs have been studied extensively by many researchers [2, 28, 42, 43, 44, 45]. Definition 6 A cycle of order p, referred as C p , can be defined as a graph with vertex set fv 0 ; v 1 ; v p Gamma1 g and for each vertex v i , 0 i p, we have (v i ; v (i 1) mod p ) 2 E(C p ) A C 16 is shown in Figure 4.1. Definition 7 1 A r regular crown, called r crown, of ....

....shown in Figure 4.6. The edge (0,1) in Figure 4.6 is called the first FC from vertex 0 and the same edge is called as the first BC from vertex 1. First let us consider a pair of vertices, say v i and v i 2 , that are distance two apart in C p . Since crowns are known to be point symmetric graphs [42], without loss of generality, we assume that v i is an even vertex. To prove that there are k edge disjoint paths of length two between v i and v i 2 , 45 i 3 i 2j 1 0 1 i 1 i i 2 i 2k 1 k 1 j Figure 4.7: A set of k edge disjoint paths between v i and v i 2 of length 2 in a (k 1) crown. i i 3 ....

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F. Boesch and R. Tindell, "Connectivity and symmetry in graphs," Graphs and Applications, Proceedings of 1st Colorado Symposium on Graph Theory, pp. 53--67, 1982.

.... Phi Phi Phi Phi Phi Phi Phi Phi Phi Phi Phi H H H H H H H H H H H H 3 1 1 1 2 3 1 2 1 2 1 2 3 3 2 3 3 1 3 3 1 2 3 3 2 1 2 1 1 2 1 2 3 3 2 2 Figure 2: A V symmetric graph. Example 2 Consider the labeled graph (I; ffi) shown in Figure 2 (also called minimum identity graph [3]) This graph is V symmetric. In fact, the labeling ffi is symmetric with the following function : 1) 2, 2) 1 and (3) 3. Moreover, ffi uses only 3 labels. By Theorem 1, the graph is completely symmetric. 4 Surroundings and S Symmetries 4.1 Surroundings We now recall the concept of ....

F. Boesch and R. Tindell. Connectivity and symmetry in graphs. In F. Harary and J.S. Maybee, editors, Graphs and Applications, pages 53--67. John Wiley and Sons, 1984.

....u 0 = u 0 fi iff v 0 = v 0 fi, that proves 2) It now follows from Theorem 7 that N(v) N(u) 2 In Figure 2 b) there is an example of a V symmetric graph (G; which is not S k symmetric for any k n where n is the number of nodes. Notice that G (known as minimum identity graph [3]) cannot be S k symmetric for k n regardless of the choice of the labeling because there are no isomorphisms between vertices in G. We shall call any such graph surrounding asymmetric. An interesting open question is the characterization of these graphs and their properties. 5 Symmetries and ....

F. Boesch and R. Tindell. Connectivity and symmetry in graphs. In Graphs and Applications (1984), F. Harary and J. Maybee, Eds., John Wiley and Sons, pp. 53--67.

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Boesch, F., Tindell, R.: Connectivity and symmetry in graphs. In: Graphs and applications (Boulder, Colo., 1982). Wiley-Intersci. Publ. Wiley, New York (1985) 53--67

No context found.

F. Boesch and R. Tindell. Connectivity and symmetry in graphs. In Graphs and applications (Boulder, Colo., 1982.

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