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All Journal Electronic Journal of Graph Theory and Applications (EJGTA)
Martin Baca
Department of Applied Mathematics and Informatics, Technical University, Kosice, Slovak Republic
Electrical & Electronics Engineering

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On total edge product cordial labeling of fullerenes Martin Baca; Muhammad Irfan; Aisha Javed; Andrea Semanicova-Fenovcikova
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 6, No 2 (2018): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/ejgta.2018.6.2.4

Abstract

For a simple graph G = (V, E) this paper deals with the existence of an edge labeling φ : E(G) → {0, 1, …, k − 1}, 2 ≤ k ≤ ∣E(G)∣, which induces a vertex labeling φ *  : V(G) → {0, 1, …, k − 1} in such a way that for each vertex v, assigns the label $\varphi(e_1)\cdot\varphi(e_2)\cdot\ldots\cdot \varphi(e_n) \pmod k$, where e1, e2, …, en are the edges incident to the vertex v. The labeling 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, $0 \le i < j \le k-1$, where eφ(i) and vφ * (i) is the number of edges and vertices with φ(e) = i and φ * (v) = i, respectively. The paper examines the existence of such labelings for toroidal fullerenes and for Klein-bottle fullerenes.
On H-irregularity strengths of G-amalgamation of graphs Faraha Ashraf; Martin Baca; Andrea Semanicova-Fenovcikova; Ayesha Shabbir
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 5, No 2 (2017): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/ejgta.2017.5.2.13

Abstract

A simple graph G=(V(G),E(G)) admits an H-covering if every edge in E(G) belongs at least to one subgraph of G isomorphic to a given graph H. Then the graph G admitting H-covering admits an H-irregular total k-labeling f: V(G) U E(G) \to {1, 2, ..., k} if for every two different subgraphs H' and H'' isomorphic to H there is $wt_{f}(H') \neq wt_{f}(H'')$, where $wt_{f}(H)= \sum \limits_{v\in V(H)} f(v) + \sum \limits_{e \in E(H)} f(e)$ is the associated H-weight. The minimum k for which the graph G has an H-irregular total k-labeling is called the total H-irregularity strength of the graph G.In this paper, we obtain the precise value of the total H-irregularity strength of G-amalgamation of graphs.
Co-Authors Aisha Javed Andrea Semanicova-Fenovcikova Ayesha Shabbir Faraha Ashraf Muhammad Irfan