Δ-optimum exclusive sum labeling of certain graphs with radius one
Indonesia-Japan Joint Conference on Combinatorial Geometry and Graph Theory, 2003•Springer
A mapping L is called a sum labeling of a graph H (V (H), E (H)) if it is an injection from V (H)
to a set of positive integers, such that xy∈ E (H) if and only if there exists a vertex w∈ V (H)
such that L (w)= L (x)+ L (y). In this case, w is called a working vertex. We define L as an
exclusive sum labeling of a graph G if it is a sum labeling of G∪̄K_r for some non negative
integer r, and G contains no working vertex. In general, a graph G will require some isolated
vertices to be labeled exclusively. The least possible number of such isolated vertices is …
to a set of positive integers, such that xy∈ E (H) if and only if there exists a vertex w∈ V (H)
such that L (w)= L (x)+ L (y). In this case, w is called a working vertex. We define L as an
exclusive sum labeling of a graph G if it is a sum labeling of G∪̄K_r for some non negative
integer r, and G contains no working vertex. In general, a graph G will require some isolated
vertices to be labeled exclusively. The least possible number of such isolated vertices is …
Abstract
A mapping L is called a sum labeling of a graph H(V(H),E(H)) if it is an injection from V(H) to a set of positive integers, such that xy ∈ E(H) if and only if there exists a vertex w ∈ V(H) such that L(w) = L(x) + L(y). In this case, w is called a working vertex. We define L as an exclusive sum labeling of a graph G if it is a sum labeling of for some non negative integer r, and G contains no working vertex. In general, a graph G will require some isolated vertices to be labeled exclusively. The least possible number of such isolated vertices is called exclusive sum number of G; denoted by ε(G).
An exclusive sum labeling of a graph G is said to be optimum if it labels G exclusively by using ε(G) isolated vertices. In case ε (G) = Δ (G), where Δ(G) denotes the maximum degree of vertices in G, the labeling is called Δ-optimum exclusive sum labeling.
In this paper we present Δ-optimum exclusive sum labeling of certain graphs with radius one, that is, graphs which can be obtained by joining all vertices of an integral sum graph to another vertex. This class of graphs contains infinetely many graphs including some populer graphs such as wheels, fans, friendship graphs, generalised friendship graphs and multicone graphs.
Springer
以上显示的是最相近的搜索结果。 查看全部搜索结果