On 3-total edge product cordial labeling of a carbon nanotube network
For a simple graph G=(V,E)with the vertex set Vand the edge set Eand for an integer k, 2≤k≤|E(G)|, an edge labeling φ:E(G)→{0,1,…,k−1}induces a vertex labeling φ∗:V(G)→{0,1,…,k−1}defined by φ∗(v)=φ(e1)⋅φ(e2)⋅…⋅φ(en)(modk), where e1,e2,…,enare the edges incident to the vertex v. The function φ is cal...
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doaj-8142845f334c411cab8110ecab9033d72020-11-25T02:56:31ZengTaylor & Francis GroupAKCE International Journal of Graphs and Combinatorics0972-86002019-12-01163310318On 3-total edge product cordial labeling of a carbon nanotube networkMartin Bača0Muhammad Irfan1Andrea Semaničová-Feňovčíková2Abdus Salam School of Mathematical Sciences, GC University, Lahore, Pakistan; Department of Applied Mathematics and Informatics, Technical University, Košice, Slovakia; Corresponding author at: Department of Applied Mathematics and Informatics, Technical University, Košice, Slovakia.Abdus Salam School of Mathematical Sciences, GC University, Lahore, PakistanAbdus Salam School of Mathematical Sciences, GC University, Lahore, Pakistan; Department of Applied Mathematics and Informatics, Technical University, Košice, SlovakiaFor a simple graph G=(V,E)with the vertex set Vand the edge set Eand for an integer k, 2≤k≤|E(G)|, an edge labeling φ:E(G)→{0,1,…,k−1}induces a vertex labeling φ∗:V(G)→{0,1,…,k−1}defined by φ∗(v)=φ(e1)⋅φ(e2)⋅…⋅φ(en)(modk), where e1,e2,…,enare the edges incident to the vertex v. The function φ is called a k-total edge product cordial labeling of G if |(eφ(i)+vφ∗(i))−(eφ(j)+vφ∗(j))|≤1 for every i,j, 0≤i<j≤k−1, where eφ(i)and vφ∗(i)are the number of edges and vertices with φ(e)=i and φ∗(v)=i, respectively.In this paper, we investigate the 3-total edge product cordial labeling of a carbon nanotube network. Keywords: Cordial labeling, k-total edge product cordial labeling, Carbon nanotube networkhttp://www.sciencedirect.com/science/article/pii/S0972860017301287 |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Martin Bača Muhammad Irfan Andrea Semaničová-Feňovčíková |
spellingShingle |
Martin Bača Muhammad Irfan Andrea Semaničová-Feňovčíková On 3-total edge product cordial labeling of a carbon nanotube network AKCE International Journal of Graphs and Combinatorics |
author_facet |
Martin Bača Muhammad Irfan Andrea Semaničová-Feňovčíková |
author_sort |
Martin Bača |
title |
On 3-total edge product cordial labeling of a carbon nanotube network |
title_short |
On 3-total edge product cordial labeling of a carbon nanotube network |
title_full |
On 3-total edge product cordial labeling of a carbon nanotube network |
title_fullStr |
On 3-total edge product cordial labeling of a carbon nanotube network |
title_full_unstemmed |
On 3-total edge product cordial labeling of a carbon nanotube network |
title_sort |
on 3-total edge product cordial labeling of a carbon nanotube network |
publisher |
Taylor & Francis Group |
series |
AKCE International Journal of Graphs and Combinatorics |
issn |
0972-8600 |
publishDate |
2019-12-01 |
description |
For a simple graph G=(V,E)with the vertex set Vand the edge set Eand for an integer k, 2≤k≤|E(G)|, an edge labeling φ:E(G)→{0,1,…,k−1}induces a vertex labeling φ∗:V(G)→{0,1,…,k−1}defined by φ∗(v)=φ(e1)⋅φ(e2)⋅…⋅φ(en)(modk), where e1,e2,…,enare the edges incident to the vertex v. The function φ is called a k-total edge product cordial labeling of G if |(eφ(i)+vφ∗(i))−(eφ(j)+vφ∗(j))|≤1 for every i,j, 0≤i<j≤k−1, where eφ(i)and vφ∗(i)are the number of edges and vertices with φ(e)=i and φ∗(v)=i, respectively.In this paper, we investigate the 3-total edge product cordial labeling of a carbon nanotube network. Keywords: Cordial labeling, k-total edge product cordial labeling, Carbon nanotube network |
url |
http://www.sciencedirect.com/science/article/pii/S0972860017301287 |
work_keys_str_mv |
AT martinbaca on3totaledgeproductcordiallabelingofacarbonnanotubenetwork AT muhammadirfan on3totaledgeproductcordiallabelingofacarbonnanotubenetwork AT andreasemanicovafenovcikova on3totaledgeproductcordiallabelingofacarbonnanotubenetwork |
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