A new sufficient condition for Hamiltonicity of graphs

Degree with Neighborhood Conditions and Highly Hamiltonian Graphs

“…In 2006, Li [6] obtained that if min{|N(u)| + N(v)| + d(u, v) : u, v ∈ V (G), uv ∈ E(G)} ≥ n + 2, then graph G is pancyclic or K n/2,n/2 . In this paper we define weakly vertex-pancyclic as generalizing the pancyclic and consider the generalizing condition and obtain that if OF = min{|N(u) ∪ N(v)| + d(w) : u, v, w ∈ V (G), uv ∈ E(G), wu, or wv ∈ E(G)} ≥ n + 1, then graph G is weakly vertex-pancyclic.…”

A sufficient condition for pancyclic graphs

“…Combining (3) and (4), we have d( In order to prove the below results, we need the following Theorem 2.3 that was proved by Rao Li [3] and Shengjia Li et al [4]. Proof.…”

“…In 2005, Rahman and Kaykobad [5] [3] two classes C n and D n of graphs of order n are defined as follows. A graph G of order n belongs to the family C n if the vertex set of G is…”

Sufficient Conditions for Hamiltonicity in Communication Networks through Graph Modeling: New Research Challenges

“…A strongly connected digraph with n vertices is Hamiltonian if the degree of each vertex is at least n. In [1], a new proposed sufficient condition is given for a graph to contain Hamiltonicity property. Suppose G is a graph having n finite vertices and e edges.…”