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摘要
Graph labelings is an active area of research in Graph Theory. There are many types of graph labelings which have been considered in recent years. A graph G(p, q) is said to be (1,1) edge-magic with the common edge count /co if there exists a bijection f : V (G) boolean OR E(G) -> {1,.,p + q} such that f (u) + f (v) + f(e) = k(0) for all e = (u, v) is an element of E(G). A graph G(p, q) is said to be (1,1) vertex-magic with the common vertex number count k1 if there exists a bijection f : V (G) U E(G) {1,..,p + q} such that for each u E V (G), f (u) + Ee f (e) = k1 for all e = (u, v) E E(G) with V is an element of V (G). A graph G(p, q) is said to be (1,0) edge-magic with the common edge count k(2) if there exists a bijection f : V(C) {1,.,p} such that for all e = (u, v) E is an element of (G), f (u) + f (v) = k(2). A graph G(p, q) is said to be (0, 1) vertex-magic with the common vertex count k(3) if there exists a bijection f : E(G) + {1,, q} such that for each u is an element of V (G), Ee f() = k(3) for all e = (u, v) E E(G) with u E V (G). A graph G(p, q) is said to be (1,0) vertex-magic with the common vertex count k(4) there exists a bijection f: V (G) {1,,p} such that for each u is an element of V (G), f (u) + f (v) = k(4) for all v is an element of V (G) such that (u, v) E is an element of (G). A graph G(p, q) is said to be (0, 1) edge-magic with the common edge-count k5 if there exists a bijection f: E(C) {1,, q} such that for each e is an element of E(G), f (e)+ f (e) = k(5) for all e is an element of E (G) such that e and e(0) are adjacent in G. The author has introduced a variety of graph labelings in [12]. In this paper, a number of interesting general results concerning these labelings are obtained.
- 出版日期2013-11
