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INDONESIA
Electronic Journal of Graph Theory and Applications (EJGTA)
Published by Indonesian Combinatorial Society
ISSN : 23382287     EISSN : -     DOI : -
Core Subject : Engineering,
Electrical & Electronics Engineering
The Electronic Journal of Graph Theory and Applications (EJGTA) is a refereed journal devoted to all areas of modern graph theory together with applications to other fields of mathematics, computer science and other sciences. The journal is published by the Indonesian Combinatorial Society (InaCombS), Graph Theory and Applications (GTA) Research Group - The University of Newcastle - Australia, and Faculty of Mathematics and Natural Sciences - Institut Teknologi Bandung (ITB) Indonesia. Subscription to EJGTA is free. Full-text access to all papers is available for free. All research articles as well as surveys and articles of more general interest are welcome. All papers will be refereed in the normal manner of mathematical journals to maintain the highest standards. This journal is sponsored by CARMA (Computer-Assisted Research Mathematics and its Applications) Priority Research Centre - The University of Newcastle - Australia, and Study Program of Information System- University of Jember - Indonesia.
Arjuna Subject : -
Articles 382 Documents
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D-antimagic labelings arising from completely separating systems Wulandari, Risma Yulina; Simanjuntak, Rinovia; Saputro, Suhadi Wido
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 13, No 2 (2025): 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.2025.13.2.2

Abstract

Let D be a non-empty subset of the distance set {0,1,…, diam(G)}. A graph G is D-antimagic if there exists a bijection f:V(G)→{1,2,…,|V(G)|} such that for every pair of distinct vertices x and y, wD(x) ≠ wD(y), where wD(x) = Σz∈ND(x)f(z) is the D-weight of x and ND(x) = {z|d(x,z)∈D} is the D-neighbourhood of x. It was conjectured that a graph G is D-antimagic if and only if each vertex in G has a distinct D-neighborhood. A completely separating system (CSS) in the finite set {1,2,…,n} is a collection ? of subsets of {1,2,…,n} in which for each pair a≠b∈{1,2,…,n}, there exist A,B∈? such that a∈A−B and b∈B−A.In this paper, we provide evidence to support the conjecture mentioned earlier by using Roberts' completely separating systems to define D-antimagic labelings for certain graphs. In particular, we show that if G and H are D-antimagic graphs with labelings constructed from Roberts' CSS, then the vertex-deleted subgraph, G−{v} and the vertex amalgamation of G and H are also D-antimagic. Additionally, we partially answer an open problem of Simanjuntak et al. (2021) by constructing {1}-antimagic labelings for some disjoint unions of paths.
Perfect coalition in graphs Mojdeh, Doost Ali; Samadzadeh, Mohammad Reza
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 13, No 2 (2025): 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.2025.13.2.8

Abstract

A perfect dominating set in a graph G = (V, E) is a subset S ⊆ V such that each vertex in V \ S has exactly one neighbor in S. A perfect coalition in G consists of two disjoint sets of vertices V1 and V2 such that i) neither V1 nor V2 is a dominating set, ii) each vertex in V(G) \ V1 has at most one neighbor in V1 and each vertex in V(G) \ V2 has at most one neighbor in V2, and iii) V1 ∪ V2 is a perfect dominating set. A perfect coalition partition (abbreviated prc-partition) in a graph G is a vertex partition π = {V1, V2, …, Vk} such that for each set Vi of π, either Vi is a singleton dominating set or there exists a set Vj ∈ π that forms a perfect coalition with Vi. In this paper, we initiate the study of perfect coalition partitions in graphs. We obtain a bound on the number of perfect coalitions involving each member of a perfect coalition partition, in terms of maximum degree. The perfect coalition of some special graphs are investigated. Graphs with minimum degree one, triangle-free graphs and trees with large perfect coalition numbers are investigated.
Quasi perfect codes in the cartesian product of some graphs Mane, Smruti; Shinde, Neeta
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 13, No 2 (2025): 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.2025.13.2.14

Abstract

An important question in the study of quasi-perfect codes is whether such codes can be constructed for all possible lengths n. In this paper, we address this question for specific values of n. First, we investigate the existence of quasi-perfect codes in the Cartesian product of a graph G and a path (or cycle), assuming that G admits a perfect code. Second, we explore quasi-perfect codes in the Cartesian products of two or three cycles, Cm□Cn and Cm□Cn□Cl, as well as in the Cartesian products of two or three paths, Pm□Pn and Pm□Pn□Pl.
The locating chromatic number of (k,n)-split cycle graph and its barbell operation Asmiati, Asmiati; Prawinasti, Kasandra; Damayanti, Maharani; Yulianti, Lyra
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 13, No 2 (2025): 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.2025.13.2.3

Abstract

The locating chromatic number remains an active topic in graph theory. It combines the concepts of partition dimension and proper vertex coloring. A necessary condition for determining the locating chromatic number is that each vertex must have a unique color code under a minimal coloring. This paper investigates the locating chromatic number of the (k,n)-split cycle graph and its barbell operation.
The Italian bondage and reinforcement numbers of digraphs Kim, Kijung
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 13, No 2 (2025): 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.2025.13.2.9

Abstract

An Italian dominating function on a digraph D with vertex set V(D) is defined as a function f : V(D) → {0, 1, 2} such that every vertex v ∈ V(D) with f(v) = 0 has at least two in-neighbors assigned 1 under f or one in-neighbor w with f(w) = 2. The weight of an Italian dominating function f is the value ω(f) = f(V(D)) = ∑u∈V(D) f(u). The Italian domination number of a digraph D, denoted by γI(D), is the minimum taken over the weights of all Italian dominating functions on D. The Italian bondage number of a digraph D, denoted by bI(D), is the minimum number of arcs of A(D) whose removal in D results in a digraph D′ with γI(D′) > γI(D). The Italian reinforcement number of a digraph D, denoted by rI(D), is the minimum number of extra arcs whose addition to D results in a digraph D′ with γI(D′) < γI(D). In this paper, we initiate the study of Italian bondage and reinforcement numbers in digraphs and present some bounds for bI(D) and rI(D). We also determine the Italian bondage and reinforcement numbers of some classes of digraphs.
Uniquely proper distinguishing colorable graphs Korivand, Meysam; Soltankhah, Nasrin; Khashyarmanesh, Kazem
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 13, No 2 (2025): 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.2025.13.2.15

Abstract

A proper vertex-coloring of a graph G is called distinguishing, if the only automorphism preserving the colors is the identity. The minimum number of colors for such a coloring is denoted by χD(G). We say a graph G is uniquely proper distinguishing colorable (UPDC, for short) if and only if there exists only one partition of V(G) into χD(G) independent sets such that the identity is the only automorphism of G preserving the partition.In this paper, we study the UPDC graphs. We show that a disconnected graph is UPDC if and only if it is the union of two isomorphic asymmetric connected bipartite graphs. We prove some results on bipartite UPDC graphs and show that any UPDC tree is one of the following: (i) an asymmetric tree, (ii) a tree with precisely one non-trivial automorphism and center xy such that this automorphism interchanges x and y, (iii) a star graph. Additional, a characterization of all graphs G of order n with the property that χD(G∪G) = χD(G) = k, where k=n-2, n-1, n, is given in this paper. Finally, we determine all graphs G of order n with the property that χD(G∪G) = χD(G)+1 = ℓ, where ℓ=n-1, n, n+1.
On Radenković and Gutman conjecture for some classes of trees of diameter 5 Maryam, Afeefa; Rahim, M. Tariq; Hussain, Fawad
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 13, No 2 (2025): 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.2025.13.2.4

Abstract

The Radenković and Gutman conjecture establishes a relationship between the Laplacian energies of any tree Tn, the star graph Sn and the path graph Pn, i.e., LE(Pn) ≤ LE(Tn) ≤ LE(Sn). In this paper, we focus on verifying the validity of this conjecture for some classes of trees with diameter 5. By analyzing their structural properties and the corresponding Laplacian spectra, we establish that the conjecture holds for these few subclasses.
Minimally 4-restricted edge connected graphs Kamyab, Khalid; Ghasemi, Mohsen; Varmazyar, Rezvan
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 13, No 2 (2025): 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.2025.13.2.10

Abstract

Suppose that G is minimally 4-restricted edge connected graph without triangle, δ(G) ≥ 2 and α4(G) ≥ 6. Suppose that A is a λ4-atom of G such that for each path of length 3 in A, say P3 = xyz, we have dA(y) − 1 = dA−{x,y,z}(y), where x ∼ y ∼ z. In this paper, under these assumptions, we show that all atoms of G are trivial.
On the sigma chromatic number of the ideal-based zero divisor graphs of the ring of integers modulo n Garciano, Agnes D.; Marcelo, Reginaldo M.; Ruiz, Mari-Jo P.; Tolentino, Mark Anthony Cayanan
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 13, No 2 (2025): 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.2025.13.2.5

Abstract

The objective of this paper is to investigate a particular graph coloring, called sigma coloring, as applied to ideal-based zero-divisor graphs. Given a commutative ring R with (nonzero) identity and a proper ideal I of R, the graph ΓI(R) is defined as an undirected graph with vertex set { x ∈ R \ I : xy ∈ I for some y ∈ R \ I } and edge set { xy : xy ∈ I }. On the other hand, given a graph G, a sigma coloring c: V(G) → ℕ is a coloring that satisfies σ(u) ≠ σ(v) for any two adjacent vertices u,v in G, where σ(x) denotes the sum of all colors c(y) among all neighbors y of a vertex x. The sigma chromatic number of G is denoted by σ(G) and is defined as the fewest number of colors needed for a sigma coloring of G. In this paper, we completely determine the sigma chromatic number of ideal-based zero-divisor graphs of rings of integers modulo n.
On the relations among edge magic total, edge antimagic total, and ASD-antimagic graphs Pancahayani, Sigit; Simanjuntak, Rinovia; Baca, Martin; Semanicova-Fenovcıkova, Andrea; Uttunggadewa, Saladin
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 13, No 2 (2025): 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.2025.13.2.11

Abstract

Let G be a simple and finite graph of order p and size q. The graph G is said to be edge magic total (EMT) if there is a bijection λ:V(G)∪E(G)→{1,2,…,p+q} such that all edge sums λ(x)+λ(xy)+λ(y), xy∈E(G), are the same. If all edge sums are pairwise distinct, then G is called edge antimagic total (EAT). Let t be a positive integer that satisfies C(t+1,2)≤q<C(t+2,2). The graph G is said to have an ascending subgraph decomposition (ASD) if G can be decomposed into t subgraphs H1,H2,…,Ht without isolated vertices such that Hi is isomorphic to a proper subgraph of Hi+1 for 1≤i≤t−1. A graph that admits an ascending subgraph decomposition is called an ASD graph. An ASD graph G is said to be ASD-antimagic if there exists a bijection f:V(G)∪E(G)→{1,2,…,p+q} such that all subgraph weights w(Hi)=∑v∈V(Hi)f(v)+∑e∈E(Hi)f(e), 1≤i≤t, are distinct. In this paper, we provide constructions of ASD-antimagic graphs arising from EMT or EAT graphs.

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