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All Journal Electronic Journal of Graph Theory and Applications (EJGTA)
Rinovia Simanjuntak
Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Indonesia
Electrical & Electronics Engineering

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On distance labelings of 2-regular graphs Anak Agung Gede Ngurah; Rinovia Simanjuntak
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 9, No 1 (2021): 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.2021.9.1.3

Abstract

Let G  be a graph with |V(G)| vertices and ψ :  V(G) → {1, 2, 3, ... , |V(G)|} be a bijective function. The weight of a vertex v ∈ V(G) under ψ is wψ(v) = ∑u ∈ N(v)ψ(u).  The function ψ is called a distance magic labeling of G, if wψ(v) is a constant for every v ∈ V(G).  The function ψ is called  an (a,d)-distance antimagic labeling of G, if the set of vertex weights is  a, a+d, a+2d, ... , a+(|V(G)|-1)d. A graph that admits a distance magic (resp. an (a,d)-distance antimagic) labeling is called  distance magic (resp.  (a,d)-distance antimagic).  In this paper, we characterize distance magic 2-regular graphs and   (a,d)-distance antimagic some classes of 2-regular graphs.
Modular irregularity strength of vertex amalgamation and comb product path with cycle related graphs Kiki A. Sugeng; Fawwaz Chirag Sofyan; Syafrizal Sy; Nurdin Hinding; Rinovia Simanjuntak
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 14, No 1 (2026): 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.2026.14.1.4

Abstract

Consider a graph G = (V(G), E(G)), where V(G) is a nonempty set of vertices and E(G) is a set of edges. Let Zn be the group of integers modulo n, and let k be a positive integer. A modular irregular labeling of a graph G of order n is a k-edge labeling ϕ : E(G) → {1, 2, … , k}, such that an induced weight function wtϕ : V(G) → Zn is bijective. The weight function is defined as follows: wtϕ(u) = Σu ∈ N(v) ϕ(uv) (mod n) for all vertices v in V(G). The minimum value of k is called the modular irregularity strength of G, denoted as ms(G). Suppose G and H are two connected graphs, with G has order n. Vertex amalgamation of graphs G and H is a graph obtained by identifying one vertex from each graph. Suppose that o is a given vertex of H. The comb product of G ▷ H is the graph obtained by taking one copy of G and n copies of H and then attaching the vertex o of the i-th copy of H to the i-th vertex of G. In this paper, we discuss on the exact values of the modular irregularity strength for several graphs such as: vertex amalgamation of cycles; comb product path (or cycle) and cycle and comb product path (or cycle) and regular graphs.
Co-Authors Anak Agung Gede Ngurah Fawwaz Chirag Sofyan Kiki A. Sugeng Nurdin Hinding Syafrizal Sy