Topological Integer Additive Set-Sequential Graphs

Sudev Naduvath, Germina Augustine and Chithra Sudev
Additional contact information
Sudev Naduvath: Department of Mathematics, Vidya Academy of Science & Technology, Thrissur 680501, India
Germina Augustine: PG & Research Department of Mathematics, Mary Matha Arts & Science College, Mananthavady 670645, India
Chithra Sudev: Naduvath Mana, Nandikkara, Thrissur 680301, India

Mathematics, 2015, vol. 3, issue 3, 1-11

Abstract: Let \(\mathbb{N}_0\) denote the set of all non-negative integers and \(X\) be any non-empty subset of \(\mathbb{N}_0\). Denote the power set of \(X\) by \(\mathcal{P}(X)\). An integer additive set-labeling (IASL) of a graph \(G\) is an injective function \(f : V (G) \to P(X)\) such that the image of the induced function \(f^+: E(G) \to \mathcal{P}(\mathbb{N}_0)\), defined by \(f^+(uv)=f(u)+f(v)\), is contained in \(\mathcal{P}(X)\), where \(f(u) + f(v)\) is the sumset of \(f(u)\) and \(f(v)\). If the associated set-valued edge function \(f^+\) is also injective, then such an IASL is called an integer additive set-indexer (IASI). An IASL \(f\) is said to be a topological IASL (TIASL) if \(f(V(G))\cup \{\emptyset\}\) is a topology of the ground set \(X\). An IASL is said to be an integer additive set-sequential labeling (IASSL) if \(f(V(G))\cup f^+(E(G))= \mathcal{P}(X)-\{\emptyset\}\). An IASL of a given graph \(G\) is said to be a topological integer additive set-sequential labeling of \(G\), if it is a topological integer additive set-labeling as well as an integer additive set-sequential labeling of \(G\). In this paper, we study the conditions required for a graph \(G\) to admit this type of IASL and propose some important characteristics of the graphs which admit this type of IASLs.

Keywords: integer additive set-labeling; integer additive set-sequential labeling; topological integer additive set-labeling; topological integer additive set-sequential labeling (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2015
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/3/3/604/pdf (application/pdf)
https://www.mdpi.com/2227-7390/3/3/604/ (text/html)

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:gam:jmathe:v:3:y:2015:i:3:p:604-614:d:52088

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().