ترجمه مقاله نقش ضروری ارتباطات 6G با چشم انداز صنعت 4.0
- مبلغ: ۸۶,۰۰۰ تومان
ترجمه مقاله پایداری توسعه شهری، تعدیل ساختار صنعتی و کارایی کاربری زمین
- مبلغ: ۹۱,۰۰۰ تومان
Abstract
Let G = (V, E) be a finite, simple and undirected graph. The edge-magic total or vertex-magic total labeling of G is a bijection f from V(G) ∪ E(G) onto the set of consecutive integers {1, 2, . . . , |V(G)| + |E(G)|}, such that all the edge weights or vertex weights are equal to a constant, respectively. When all the edge weights or vertex weights are different then the labeling is called edge-antimagic or vertex-antimagic total, respectively. In this paper we provide some classes of graphs that are simultaneously super edge-magic total and super vertex-antimagic total, that is, graphs admitting labeling that has both properties at the same time. We show several results for fans, sun graphs, caterpillars and prisms.
3. Conclusion
In the paper we dealt with the problem of finding total labelings of some classes of graphs that are simultaneously super vertex-magic and super edge-antimagic. We showed the existence of such labelings for certain classes of graphs, namely fans, sun graphs, one class of caterpillars and prisms. In [12] authors ask not only for finding classes of graphs that are simultaneously vertex-magic and edge-antimagic but also graphs that are simultaneously vertex-antimagic and edge-magic.