WebThe connectivity of a multiprocessor system or an interconnection network plays an important role in measuring the fault tolerance of the network and the hyper petersen graph has many good properties. The connectivity of a multiprocessor system or an interconnection network plays an important role in measuring the fault tolerance of the … The Petersen graph has a Hamiltonian path but no Hamiltonian cycle. It is the smallest bridgeless cubic graph with no Hamiltonian cycle. It is hypohamiltonian, meaning that although it has no Hamiltonian cycle, deleting any vertex makes it Hamiltonian, and is the smallest hypohamiltonian graph. As a finite connected vertex-transitive graph that does not have a Hamiltonian …
Petersen graph - Encyclopedia of Mathematics
Web12. sep 2024 · As the graph has an even number of vertices, the chromatic number of the Petersen graph is 3. Chromatic Number=3 Other characteristics: It is a 3-connected graph and hence 3-edge-connected and bridgeless. It has chromatic polynomial t (t-1) (t-2) (t 7 -12t 6 +67t 5 -230t 4 +529t 3 -814t 2 +775t-352) It is Non-Planar. It is not Hamiltonian. WebThe Petersen graph is a cubic symmetric graph and is nonplanar. The following elegant proof due to D. West demonstrates that the Petersen graph is nonhamiltonian. If there is a 10-cycle , then the graph consists of … bourbon and baileys drink
The Generalized Connectivity of Generalized Petersen Graph
Web31. mar 2024 · Let G be a group. The power graph of G is a graph with vertex set G in which two distinct elements x, y are adjacent if one of them is a power of the other. We characterize all groups whose power graphs have finite independence number, show that they have clique cover number equal to their independence number, and calculate this … WebBranches of algebraic graph theory Using linear algebra. The first branch of algebraic graph theory involves the study of graphs in connection with linear algebra.Especially, it studies the spectrum of the adjacency matrix, or the Laplacian matrix of a graph (this part of algebraic graph theory is also called spectral graph theory).For the Petersen graph, for … WebThe line graph of the Petersen graph is 4-connected, claw-free and contains no cycle of length 4 (see Figure 1). Theorem 3 (Ferrara, Gould, Gehrke, Magnant, Powell [2] ). Every... bourbon and bailey\u0027s bbq