On Modular Edge-Graceful Graphs |
| |
Authors: | Futaba Fujie-Okamoto Ryan Jones Kyle Kolasinski Ping Zhang |
| |
Institution: | 1.Mathematics Department,University of Wisconsin La Crosse,La Crosse,USA;2.Department of Mathematics,Western Michigan University,Kalamazoo,USA |
| |
Abstract: | Let G be a connected graph of order \({n\ge 3}\) and size m and \({f:E(G)\to \mathbb{Z}_n}\) an edge labeling of G. Define a vertex labeling \({f': V(G)\to \mathbb{Z}_n}\) by \({f'(v)= \sum_{u\in N(v)}f(uv)}\) where the sum is computed in \({\mathbb{Z}_n}\) . If f′ is one-to-one, then f is called a modular edge-graceful labeling and G is a modular edge-graceful graph. A graph G is modular edge-graceful if G contains a modular edge-graceful spanning tree. Several classes of modular edge-graceful trees are determined. For a tree T of order n where \({n\not\equiv 2 \pmod 4}\) , it is shown that if T contains at most two even vertices or the set of even vertices of T induces a path, then T is modular edge-graceful. It is also shown that every tree of order n where \({n\not\equiv 2\pmod 4}\) having diameter at most 5 is modular edge-graceful. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|