Tutte [W.T. Tutte, On the algebraic theory of graph colorings, J. Combin. Theory 1 (1966) 15–20] conjectured that every bridgeless Petersen-minor free graph admits a nowhere-zero 4-flow. Let (P10)μ̄ be the graph obtained from the Petersen graph by contracting μ edges from a perfect matching. In this paper we prove that every bridgeless (P10)3̄-minor free graph admits a nowhere-zero 4-flow. c © 20...

A complete classification is given of vertex primitive and vertex bi-primitive s-arc regular graphs with s ≥ 3. In particular, it is shown that the Petersen graph and Coxeter graph are the only vertex primitive 3-arc regular graphs, and that vertex bi-primitive 3-arc regular graphs consist of the complete bipartite graph K3,3, the standard double covers of the Petersen graph and Coxeter graph, ...

We prove a conjecture of Saito that if a graph G with ≥ 3 has no cycle of length 1 (mod 3), then G has an induced subgraph which is isomorphic to the Petersen graph. The above result strengthened the result by Dean et al. that every 2-connected graph with ≥ 3 has a (1 mod 3)-cycle if G is not isomorphic to the Petersen graph. ? 2001 Elsevier Science B.V. All rights reserved.

We exhibit a graceful labelling for each generalised Petersen graph P8t,3 with t ≥ 1. As an easy consequence, we obtain that for any fixed t the corresponding graph is the unique starter graph for a cyclic edgedecomposition of the complete graph K2t+1. Due to its extreme versatility, the technique employed looks promising for finding new graceful labellings, not necessarily involving generalise...

Several countries of the world are involved in mutual and collaborative business military equipments, weapons terms their production, sales, technical maintenance, training services. As a consequence, manufacturing boms, rockets, missiles other ammunitions have taken structured smooth shape to help others where when needed. Often support among remain open for information media, but sometime sec...

We characterize all groups which can occur as the topological symmetry group or orientation preserving of some embedding Petersen graph in [Formula: see text].

AgraphG is k-ordered if for every sequence of k distinct vertices ofG, there exists a cycle inG containing these k vertices in the specified order. It is k-ordered-Hamiltonian if, in addition, the required cycle is a Hamiltonian cycle in G. The question of the existence of an infinite class of 3-regular 4-ordered-Hamiltonian graphs was posed in Ng and Schultz in 1997 [2]. At the time, the only ...