AbstractA graph G is n-hamiltonian (resp. n-edge hamiltonian) if after the removal of any k vertices (resp. edges) with 0⩽k⩽n, the resulting graph is hamiltonian. The kth power of a graph G is the graph having the same vertex-set as G and such that u and υ, vertices of Gk, are adjacent if and only if the distance between u and υ in G is at most k.In this paper, we prove that if G is a connected graph then Gk is (k−2)-edge hamiltonian if k⩾3 and |V(G)|k+1. Furthermore, if G is 2-connected and |V(G)|k+2 then Gk is (k−1)-edge hamiltonian
For distinct vertices u and ν of a nontrivial connected graph G, the detour distance D(u, ν) between...
For distinct vertices u and ν of a nontrivial connected graph G, the detour distance D(u, ν) between...
For distinct vertices u and ν of a nontrivial connected graph G, the detour distance D(u, ν) between...
AbstractA graph G of order p ⩾ 3 is called n-hamiltonian, 0 ⩽ n ⩽ p − 3, if the removal of any m ver...
AbstractBill Jackson has proved that every 2-connected, k-regular graph on at most 3k vertices is ha...
AbstractIt is known that if G is a connected simple graph, then G3 is Hamiltonian (in fact, Hamilton...
AbstractA graph G is called uniquely hamiltonian-connected from a vertex ν of G if G contains exactl...
summary:In this paper the following results are proved: 1. Let $P_n$ be a path with $n$ vertices, wh...
[[abstract]]Let G be a graph. For a positive integer k, the k-th power Gk of G is the graph having t...
A graph $G$ is $k$-edge-Hamiltonian if any collection of vertex-disjoint paths with at most $k$ edge...
AbstractA graph G is n-hamiltonian (resp. n-edge hamiltonian) if after the removal of any k vertices...
A graph is hamiltonian-connected if every pair of vertices can be connected by a hamiltonian path, a...
AbstractA graph G with p≥3 points, 0≤n≤p−3, is called n-Hamiltonian if the removal of any k points f...
For distinct vertices u and ν of a nontrivial connected graph G, the detour distance D(u, ν) between...
AbstractAssume that n and δ are positive integers with 3≤δ<n. Let hc(n,δ) be the minimum number of e...
For distinct vertices u and ν of a nontrivial connected graph G, the detour distance D(u, ν) between...
For distinct vertices u and ν of a nontrivial connected graph G, the detour distance D(u, ν) between...
For distinct vertices u and ν of a nontrivial connected graph G, the detour distance D(u, ν) between...
AbstractA graph G of order p ⩾ 3 is called n-hamiltonian, 0 ⩽ n ⩽ p − 3, if the removal of any m ver...
AbstractBill Jackson has proved that every 2-connected, k-regular graph on at most 3k vertices is ha...
AbstractIt is known that if G is a connected simple graph, then G3 is Hamiltonian (in fact, Hamilton...
AbstractA graph G is called uniquely hamiltonian-connected from a vertex ν of G if G contains exactl...
summary:In this paper the following results are proved: 1. Let $P_n$ be a path with $n$ vertices, wh...
[[abstract]]Let G be a graph. For a positive integer k, the k-th power Gk of G is the graph having t...
A graph $G$ is $k$-edge-Hamiltonian if any collection of vertex-disjoint paths with at most $k$ edge...
AbstractA graph G is n-hamiltonian (resp. n-edge hamiltonian) if after the removal of any k vertices...
A graph is hamiltonian-connected if every pair of vertices can be connected by a hamiltonian path, a...
AbstractA graph G with p≥3 points, 0≤n≤p−3, is called n-Hamiltonian if the removal of any k points f...
For distinct vertices u and ν of a nontrivial connected graph G, the detour distance D(u, ν) between...
AbstractAssume that n and δ are positive integers with 3≤δ<n. Let hc(n,δ) be the minimum number of e...
For distinct vertices u and ν of a nontrivial connected graph G, the detour distance D(u, ν) between...
For distinct vertices u and ν of a nontrivial connected graph G, the detour distance D(u, ν) between...
For distinct vertices u and ν of a nontrivial connected graph G, the detour distance D(u, ν) between...