A hamiltonian cycle is a spanning cycle in a graph (a cycle through every vertex). We call
that a graph G is hamiltonian if G has a hamiltonian cycle. AnalOgously, hamiltonian path is …

Let G be a simple undirected graph of order n. For an independent set S⊂ V (G) of k
vertices, we define the k neighborhood intersections Si={v ϵ V (G) &# 92; S| N (v)∩ S|= i} …

Let G=(V, E) be a k-connected graph of order n. For S⊂ V, let N (S) be its neighborhood set
and let J (S)={u∉ S| N (u)⊇ S} if| S|⩾ 2 and J (S)= 0 otherwise. If there exists some s, 1⩽ s⩽ …

Let G be a graph of order n. We show that if G is a 2‐connected graph and max {d (u), d
(v)}+| N (u) UN (v)|≥ n for each pair of vertices u, v at distance two, then either G is …

Let G and H be graphs. G is said to be degree-light H-free if G is either H-free or, for every
induced subgraph K of G with K≅ H, and every {u, v}⊆ K, dist K (u, v)= 2 implies max {d (u) …

In this paper, k+ 1 real numbers c1, c2, ⃛, ck+ 1 are found such that the following condition is
sufficient for ak‐connected graph of order n to be hamiltonian: for each independent vertex …

The purpose of this communication is to describe four new sufficient conditions for the
existence of hamiltonian circuits in graphs. We mention first ten known results. Each one can …

Graphs and Combinatorics Page 1 0-Dual Closures for Several Classes of Graphs Ahmed
Ainouche1 and Ingo Schiermeyer2 1 UAG-CEREGMIA-GRIMAAG, Campus de Schoelcher …

For two non-adjacent vertices u: v in a graph G, we use a (u~ v) to denote the ma."\. imum
cardinality of an independent vertex set of G containing both u and v. In this paper, we prove …

Dirac proved that a graph G is hamiltonian if the minimum degree δ(G)≧n/2, where n is the
order of G. Let G be a graph and A⊆V(G). The neighborhood of A is N(A)={b:ab∈E(G) for …