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...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 |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.展开更多
基金Supported by the Educational and Scientific Research Program for Middle-aged and Young Teachers of Fujian Province in 2016(JAT160593)
文摘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 |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.
