Face antimagic labelings of toroidal and Klein bottle grid graphs

Face antimagic labelings of toroidal and Klein bottle grid graphs

In this paper we deal with the problem of labeling the vertices, edges and faces of a toroidal and Klein bottle grid graphs with 4-sided faces by the consecutive integers from 1 up to + + and + + in such a way that the label of a 4-sided face and the labels of the vertices and edges surrounding that...

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Main Authors: Saad Ihsan Butt, Muhammad Numan, Sharafat Ali, Andrea Semaničová-Feňovčíková
Format: Article
Language:English
Published: Taylor & Francis Group 2020-01-01
Series:AKCE International Journal of Graphs and Combinatorics
Subjects:
toroidal grid
klein bottle grid
super -antimagic labeling
Online Access:http://dx.doi.org/10.1016/j.akcej.2018.09.005
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spelling doaj-8a5c414a6b7e4e51af3b58ad0aef08562020-12-17T17:28:37ZengTaylor & Francis GroupAKCE International Journal of Graphs and Combinatorics0972-86002543-34742020-01-0117110911710.1016/j.akcej.2018.09.0051758490Face antimagic labelings of toroidal and Klein bottle grid graphsSaad Ihsan Butt0Muhammad Numan1Sharafat Ali2Andrea Semaničová-Feňovčíková3Department of Mathematics. COMSATS University IslamabadDepartment of Mathematics. COMSATS University IslamabadDepartment of Mathematics. COMSATS University IslamabadDepartment of Appl. Mathematics and Informatics, Technical UniversityIn this paper we deal with the problem of labeling the vertices, edges and faces of a toroidal and Klein bottle grid graphs with 4-sided faces by the consecutive integers from 1 up to + + and + + in such a way that the label of a 4-sided face and the labels of the vertices and edges surrounding that face all together add up to a weight of that face. These face-weights then form an arithmetic progression with common difference . The paper examines the existence of such labelings for several differences .http://dx.doi.org/10.1016/j.akcej.2018.09.005toroidal gridklein bottle gridsuper -antimagic labeling
collection DOAJ
language English
format Article
sources DOAJ
author Saad Ihsan Butt
Muhammad Numan
Sharafat Ali
Andrea Semaničová-Feňovčíková
spellingShingle Saad Ihsan Butt
Muhammad Numan
Sharafat Ali
Andrea Semaničová-Feňovčíková
Face antimagic labelings of toroidal and Klein bottle grid graphs
AKCE International Journal of Graphs and Combinatorics
toroidal grid
klein bottle grid
super -antimagic labeling
author_facet Saad Ihsan Butt
Muhammad Numan
Sharafat Ali
Andrea Semaničová-Feňovčíková
author_sort Saad Ihsan Butt
title Face antimagic labelings of toroidal and Klein bottle grid graphs
title_short Face antimagic labelings of toroidal and Klein bottle grid graphs
title_full Face antimagic labelings of toroidal and Klein bottle grid graphs
title_fullStr Face antimagic labelings of toroidal and Klein bottle grid graphs
title_full_unstemmed Face antimagic labelings of toroidal and Klein bottle grid graphs
title_sort face antimagic labelings of toroidal and klein bottle grid graphs
publisher Taylor & Francis Group
series AKCE International Journal of Graphs and Combinatorics
issn 0972-8600
2543-3474
publishDate 2020-01-01
description In this paper we deal with the problem of labeling the vertices, edges and faces of a toroidal and Klein bottle grid graphs with 4-sided faces by the consecutive integers from 1 up to + + and + + in such a way that the label of a 4-sided face and the labels of the vertices and edges surrounding that face all together add up to a weight of that face. These face-weights then form an arithmetic progression with common difference . The paper examines the existence of such labelings for several differences .
topic toroidal grid
klein bottle grid
super -antimagic labeling
url http://dx.doi.org/10.1016/j.akcej.2018.09.005
work_keys_str_mv AT saadihsanbutt faceantimagiclabelingsoftoroidalandkleinbottlegridgraphs
AT muhammadnuman faceantimagiclabelingsoftoroidalandkleinbottlegridgraphs
AT sharafatali faceantimagiclabelingsoftoroidalandkleinbottlegridgraphs
AT andreasemanicovafenovcikova faceantimagiclabelingsoftoroidalandkleinbottlegridgraphs
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