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 |ef(1)-ef(-1)| ≤ 1and [vf(1)-vf(-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.
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