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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 398 Documents
 36   37   38   39   40 
Graceful labeling of zero-divisor graph Γ(ℤp²q) and Γ(ℤp³q) Constantine, Christian; Suwastika, Erma
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.2025.13.2.6

Abstract

Some papers have already provided graceful labeling for some types of zero-divisor graphs. We reviewed the graceful labeling results of Γ(ℤ25), Γ(ℤ8), and Γ(ℤ27), then use those results to label zero-divisors graphs Γ(ℤ25q), Γ(ℤ8q), and Γ(ℤ27q).The result is that there is graceful labeling for Γ(ℤp²q) for p = 5 and Γ(ℤp³q) for p = 2, 3, where q is prime number that is different from p. In this paper, we provide the graceful labeling of zero-divisor graph Γ(ℤp²q) and Γ(ℤp³q) with adaptation and modification of existing results.
On adjacency and (signless) Laplacian spectra of centralizer and co-centralizer graphs of some finite non-abelian groups Kalita, Jharna; Paul, Somnath
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.2025.13.2.12

Abstract

Let G be a finite non-abelian group. The centralizer graph of G is a simple undirected graph Γcent(G), whose vertices are the proper centralizers of G and two vertices are adjacent if and only if their cardinalities are identical. The complement of the centralizer graph is called the co-centralizer graph. In this paper, we investigate the adjacency and (signless) Laplacian spectra of centralizer and co-centralizer graphs of some classes of finite non-abelian groups and obtain some conditions on a group so that the centralizer and co-centralizer graphs are adjacency, (signless) Laplacian integral. We also demonstrate how the integrality phenomena of these graphs either align with or differ from those of the commuting and non-commuting graphs of the corresponding groups.
The mincut graph of a graph Kriel, Christo; Mphako-Banda, Eunice
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.2026.14.1.3

Abstract

In this paper we introduce an intersection graph of a graph G, with vertex set the minimum edge-cuts of G. We find the minimum cut-set graphs of some well-known families of graphs and study the mincut graph as a graph operator. In doing so we follow the research programme on graph operators, as introduced by Prisner in the 1995 monograph "Graph Dynamics". Thus we ask and attempt to answer questions such as 'Which graphs appear as images of graphs?'; 'Which graphs are fixed under the operator?'; 'What happens if the operator is iterated?' We show that every graph is a minimum cut-set graph, henceforth called a mincut graph, of infinite depth and with an infinite number of roots.
Analogues of Bermond-Bollobás conjecture for cages yield expander families Eze, Leonard Chidiebere; Jajcay, Robert
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.2026.14.1.9

Abstract

This paper presents a possible link between Cages and Expander Graphs by introducing three interconnected variants of the Bermond and Bollobás Conjecture, originally formulated in 1981 within the context of the Degree/Diameter Problem. We adapt these conjectures to cages, with the most robust variant posed as follows: Does there exist a constant c such that for every pair of parameters k,g there exists a k-regular graph of girth g and order not exceeding M(k,g) + c?; where M(k,g) denotes the value of the so-called Moore bound for cages. We show that a positive answer to any of the three variants of the Bermond and Bollobás Conjecture for cages considered in our paper would yield for all k ≥ 3 the existence of k-regular expander graphs with Cheeger constant asymptotically bounded below by 1/(k-1) (expander families); thereby establishing a connection between Cages and Expander Graphs.
Decompositions and packings in truncated triangulations Muzheve, Michael
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.2026.14.1.15

Abstract

We study decompositions and packings in truncated triangulations GT△ obtained from simple connected plane graphs G with minimum degree two. We show GT△ is a 3-connected cubic planar graph with at least 2|E(G)|² - 2|E(G)| + 1 perfect matchings, a Λ-factor, and can be decomposed into a union of C₆'s and K₂'s if G is bipartite. Additionally, we show that GT△ is hamiltonian if G is bipartite with a dominating path P satisfying, for any e = xy ∉ E(P) exactly one of x and y is in V(P). We also prove a result giving necessary and sufficient conditions for the hamiltonicity of GT△. Additional results include showing that a truncated triangulation of a cubic plane bipartite graph G has a hamiltonian cycle that separates specific faces of GT△ if and only if the triangulation G△ has an A-trail.
Modular irregularity strength of vertex amalgamation and comb product path with cycle related graphs Sugeng, Kiki A.; Sofyan, Fawwaz Chirag; Sy, Syafrizal; Hinding, Nurdin; Simanjuntak, Rinovia
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.
Odd order C₄-face-magic projective grid graphs Curran, Stephen James
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.2026.14.1.10

Abstract

For a graph G = (V, E) embedded in the projective plane, let F(G) denote the set of faces of G. Then, G is called a Cₙ-face-magic projective graph if there exists a bijection f: V(G) → {1, 2, …, |V(G)|} such that for any F ∈ F(G) with F ≅ Cₙ, the sum of all the vertex labels around Cₙ is a constant S. We consider the m × n grid graph, denoted by Pm,n, embedded in the projective plane in the natural way.Let m ≥ 3 and n ≥ 3 be odd integers. It is known that the C₄-face-magic value of a C₄-face-magic labeling on Pm,n is either 2mn+1, 2mn+2, or 2mn+3. The characterization of C₄-face-magic labelings on Pm,n having C₄-face-magic value 2mn+2 is known. In this paper, we determine a category of C₄-face-magic labelings on Pm,n for which the C₄-face-magic value is either 2mn+1 or 2mn+3. It is conjectured that these are the only C₄-face-magic labelings on Pm,n having C₄-face-magic value 2mn+1 or 2mn+3.
Computation of the eigenvalues of complete signed graphs Pirzada, Shariefuddin; Ul Rashid, Mir Riyaz; Rehman, Amir; Baskoro, Edy Tri
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.2026.14.1.16

Abstract

A signed graph Σ is the ordered pair (G,σ), where G=(V,E) is a finite simple graph, called the underlying graph, and σ: E(G) → {+1, -1} is a sign function or a signature of Σ. Let (K_n,σ) be a complete signed graph with n vertices. In this paper, we give a complete description of the adjacency, Laplacian and net Laplacian spectrum of a complete signed graph (K_n,σ) whenever its negative edges induce either a complete tripartite graph or a friendship graph. This is an addition to the class of complete signed graphs whose spectra is completely known.
New bounds on the connected-pseudoachromatic index of complete graphs Cervantes-Ojeda, Jorge; Gómez-Fuentes, María C.; Rubio-Montiel, Christian
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.2026.14.1.5

Abstract

We improve several previously known bounds of the connected-pseudoachromatic index of complete graphs. We apply a Rank Genetic Algorithm to find experimental solutions above the known lower bounds and then we obtain an approximation of the upper bound to verify and compare to the empirically obtained results.
A special case of the tree packing conjecture Gubanyi, Marcus E
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.2026.14.1.11

Abstract

The Tree Packing Conjecture of Gyárfás states that for any set of n-1 trees T = {T₁, T₂, …, Tn-1}, where Ti has i edges, T can be packed into Kn. We define a family of trees called two-spiders that are almost stars, and show that packings of Kn with two-spiders can be constructed by exchanging edges of known packings. We prove that if each tree Ti ∈ T is a two-spider and has at most α i two-legs for α = (3-√5)/4, then T packs into Kn.

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