AbstractIn this note, we give a new short proof of the following theorem: Let G be a 2-connected graph of order n. If for any two vertices u and v with d(u,v)=2, max{d(u),d(v)}⩾c/2, then the circumference of G is at least c, where 3⩽c⩽n and d(u,v) is the distance between u and v in G
Let Gt(n) be the class of connected graphs on n vertices having the longest cycle of length t and ...
AbstractN. Alon [J. Graph Theory 10 (1986), 123–127] proved that if the minimum degree of a graph G ...
AbstractLet k be a positive integer and let G be a graph with |V(G)|⩾k+1. For two distinct vertices ...
AbstractIn this note, we give a short proof of the following theorem: if G is a 2-connected graph of...
AbstractIn this note, we give a new short proof of the following theorem: Let G be a 2-connected gra...
Let Gt(n) be the class of connected graphs on n vertices having the longest cycle of length t and le...
AbstractWe prove that a 2-connected graph G of order p is traceable if |N(u)∪N(v)| − |N(w)∪N(x)| ⩾ p...
AbstractThe codiameter of a graph is defined as the minimum, taken over all pairs of vertices u and ...
For $n\in \mathbb{N}$ and $D\subseteq \mathbb{N}$, the distance graph $P_n^D$ has vertex set $\{ 0,1...
AbstractA path P of a graph G is called a Dλ-path if every component of G/V(P) has order less than λ...
We will classify all finite simple graphs whose 2-distance graph have large or small maximum valenc...
AbstractLet G be a graph. The connectivity of G, κ(G), is the maximum integer k such that there exis...
For $n\in \mathbb{N}$ and $D\subseteq \mathbb{N}$, the distance graph $P_n^D$ has vertex set $\{ 0,1...
AbstractLet C be a longest cycle in a connected graph G and L(G) the length of the longest path in G...
AbstractFor a graph G of order n≥3 define P(k), 3≤k≤n, to be the following property: dG(x, y) = 2 ⇒ ...
Let Gt(n) be the class of connected graphs on n vertices having the longest cycle of length t and ...
AbstractN. Alon [J. Graph Theory 10 (1986), 123–127] proved that if the minimum degree of a graph G ...
AbstractLet k be a positive integer and let G be a graph with |V(G)|⩾k+1. For two distinct vertices ...
AbstractIn this note, we give a short proof of the following theorem: if G is a 2-connected graph of...
AbstractIn this note, we give a new short proof of the following theorem: Let G be a 2-connected gra...
Let Gt(n) be the class of connected graphs on n vertices having the longest cycle of length t and le...
AbstractWe prove that a 2-connected graph G of order p is traceable if |N(u)∪N(v)| − |N(w)∪N(x)| ⩾ p...
AbstractThe codiameter of a graph is defined as the minimum, taken over all pairs of vertices u and ...
For $n\in \mathbb{N}$ and $D\subseteq \mathbb{N}$, the distance graph $P_n^D$ has vertex set $\{ 0,1...
AbstractA path P of a graph G is called a Dλ-path if every component of G/V(P) has order less than λ...
We will classify all finite simple graphs whose 2-distance graph have large or small maximum valenc...
AbstractLet G be a graph. The connectivity of G, κ(G), is the maximum integer k such that there exis...
For $n\in \mathbb{N}$ and $D\subseteq \mathbb{N}$, the distance graph $P_n^D$ has vertex set $\{ 0,1...
AbstractLet C be a longest cycle in a connected graph G and L(G) the length of the longest path in G...
AbstractFor a graph G of order n≥3 define P(k), 3≤k≤n, to be the following property: dG(x, y) = 2 ⇒ ...
Let Gt(n) be the class of connected graphs on n vertices having the longest cycle of length t and ...
AbstractN. Alon [J. Graph Theory 10 (1986), 123–127] proved that if the minimum degree of a graph G ...
AbstractLet k be a positive integer and let G be a graph with |V(G)|⩾k+1. For two distinct vertices ...
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