Super magic strength of a graph

D. G. Akka and Nanda S. Warad
Additional contact information
D. G. Akka: Nadgir Institute of Engineering and Technology
Nanda S. Warad: Govt. Degree College

Indian Journal of Pure and Applied Mathematics, 2010, vol. 41, issue 4, 557-568

Abstract: Abstract By G(p, q) we denote a graph having p vertices and q edges, by V and E the vertex set and edge set of G respectively. A graph G(p, q) is said to have an edge magic labeling (valuation) with the constant (magic number) c(f) if there exists a one-to-one and onto function f: V ∪ E → {1, 2, …., p + q} such that f(u)+f(v)+f(uv) = c(f) for all uv ∈ E. An edge magic labeling f of G is called a super magic labeling if f(E) ={1, 2, …., q}. In this paper the concepts of the super magic and super magic strength of a graph are introduced. The super magic strength (sms) of a graph G is defined as the minimum of all constants c′(f) where the minimum is taken over all super magic labeling of G and is denoted by sms(G). This minimum is defined only if the graph has at least one such super magic labeling. In this paper, the super magic strength of some well known graphs P 2n , P 2n+1, K 1,n , B n,n , , P n 2 and (2n + 1)P 2, C n and W n are obtained, where P n is a path on n vertices, K 1,n is a star graph on n+1 vertices, n-bistar B n,n is the graph obtained from two copies of K 1,n by joining the centres of two copies of K 1,n by an edge e, if e is subdivided then B n,n becomes , (2n + 1) P 2 is 2n + 1 disjoint copies of P 2, P n 2 is a square graph of P n . C n is a cycle on n vertices and W n = C n + K 1 is wheel on n + 1 vertices.

Keywords: Edge magic labeling; magic strength; super magic strength; super edge magic strength (search for similar items in EconPapers)
Date: 2010
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s13226-010-0031-z Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:indpam:v:41:y:2010:i:4:d:10.1007_s13226-010-0031-z

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/13226

DOI: 10.1007/s13226-010-0031-z

Access Statistics for this article

Indian Journal of Pure and Applied Mathematics is currently edited by Nidhi Chandhoke

More articles in Indian Journal of Pure and Applied Mathematics from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().