Some new formulae on Δ–optimum exclusive sum labeling of certain trees
| Autor: | Debdas Mishra, R. K. Samal |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
Discrete mathematics
Algebra and Number Theory Graph labeling Applied Mathematics Edge-graceful labeling 0102 computer and information sciences 02 engineering and technology 01 natural sciences Negative integer Graph Vertex (geometry) Combinatorics 010201 computation theory & mathematics 0202 electrical engineering electronic engineering information engineering 020201 artificial intelligence & image processing Bound graph Analysis Mathematics |
| Zdroj: | Journal of Discrete Mathematical Sciences and Cryptography. 19:397-403 |
| ISSN: | 2169-0065 0972-0529 |
| DOI: | 10.1080/09720529.2015.1102958 |
| Popis: | All sum graphs are disconnected. The notions of sum labeling and sum graphs were introduced by Harary [1] and later extended to include all integers [2]. A mapping L is called a sum labeling 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 call L as an exclusive sum labeling of a graph G if it is 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 ∈(G). An exclusive sum labeling of a graph G is said to be optimum if it labels G exclusively by using ∈(G) isolated vertices. In case ∈(G)=Δ(G), where D(G) denotes the maximum degree of vertices in G, the labeling is called Δ- optimum exclusive sum labeling. In this paper... |
| Databáze: | OpenAIRE |
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