关键词: H-cordial, Odd-degree graph, Semi-H-cordial

Abstract: I. Cahit calls a graph H-cordial if it is possible to label the edges with the numbers from the set{1,-1} in such a way that, for some k, at each vertex v the sum of the labels on the edges incident with v is either k or-k and the inequalities |v(k)-v(-k)| ≤ 1 and|e(1)-e(-1)| ≤ 1 are also satisfied. A graph G is called to be semi-H-cordial, if there exists a labeling f, such that for each vertex v, |f(v)| ≤ 1, and the inequalities |e_f(1)-e_f(-1)| ≤ 1 and |v_f(1)-v_f(-1)| ≤ 1 are also satisfied. An odd-degree(even-degree) graph is a graph that all of the vertex is odd(even) vertex. Three conclusions were proved:(1) An H-cordial graph G is either odd-degree graph or even-degree graph;(2) If G is an odd-degree graph, then G is H-cordial if and only if |E(G)| is even;(3) A graph G is semi-H-cordial if and only if |E(G)| is even and G has no Euler component with odd edges. 

Key words: H-cordial, Odd-degree graph, Semi-H-cordial