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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 413 Documents
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On the locating chromatic number of infinite trees Yusuf Hafidh; Devi Imulia Dian Primaskun; Edy Tri Baskoro
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 14, No 2 (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.2026.14.2.3

Abstract

The locating chromatic number of a graph is the smallest integer n such that there exists a proper n-coloring c for which every vertex has a unique vector of distances to the color classes defined by c. If no such integer n exists, the locating chromatic number is infinite. We explore properties of the locating chromatic number of infinite graphs, focusing on sufficient and necessary conditions for an infinite tree to have a finite locating chromatic number. We conjectured that an infinite tree has a finite locating chromatic number if and only if the tree has bounded degree and is prunable. We prove that the conditions in the conjecture are sufficient and provide evidence as to why they might be necessary. Lastly, we compare the performance of our locating coloring algorithm with that of known locating coloring algorithms. Our algorithm outperforms previously known algorithms for trees with many branches.
NP-completeness and an ILP formulation for the P3-convex domination problem Anjan Gautam; Biswajit Deb; Pinaki Mitra; Puran Dangal
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 14, No 2 (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.2026.14.2.9

Abstract

A set S ⊆ V(G) of a graph G is called a P3-convex dominating set if it is a dominating set and for every path u − w − v of length two with u, v ∈ S, the vertex w belongs to S. The P3-convex domination number γ3c(G) is the cardinality of a minimum P3-convex dominating set (P3-CDS). In this paper, we present several foundational results concerning this parameter. First, we show that for any integers n ≥ 6 and 1 ≤ k ≤ n, there exists a graph G of order n such that γ3c(G) = k. We then show that the P3-CONVEX DOMINATING SET decision problem is NP-complete, even when restricted to bipartite graphs. Finally, we present an integer linear programming formulation for the P3-convex dominating set problem and prove that its optimal solutions correspond exactly to minimum P3-convex dominating sets.
Outer multiset dimensions of (extended) corona product graphs Hassan Pervaiz; Rinovia Simanjuntak; Suhadi Wido Saputro
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 14, No 2 (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.2026.14.2.15

Abstract

The outer multiset dimension of graph G, dimms(G), is the cardinality of the smallest subset S of vertices that uniquely recognizes each vertex outside S using the multiset of distances between the vertex and the vertices in S. This paper considers the outer multiset dimensions of both the corona product and the extended corona product of a connected graph with one of the following: a complete graph, the complement of a complete graph, or a star.
Coloring properties of corona products in signed graphs Pie Desire Ebode Atangana; Maxwell Ndognkon Manga; Erick Patrick Zobo
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 14, No 2 (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.2026.14.2.4

Abstract

This paper studies coloring and circular coloring of signed graphs. A signed graph is a graph together with a signature that assigns to each edge a sign which is either positive or negative. This paper studies coloring properties of corona products of signed graphs, including vertex corona product, edge corona product, neighbourhood corona product. Assume (G, σ) and (H, τ) are two signed graphs. The vertex corona product, edge corona product and neighborhood corona product of (G, σ) and (H, τ) are denoted by (G ⊙ H, σ ⊙ τ), (G ⋄ H, σ ⋄ τ), and (G ⋆ H, σ ⋆ τ), respectively. We obtain the following upper bounds for their chromatic numbers: χ(G ⊙ H, σ ⊙ τ) ≤ max{χ(G, σ), χ(H, τ) + 2}, χ(G ⋄ H, σ ⋄ τ) ≤ max{χ(G, σ), χ(H, τ) + 4}, and χ(G ⋆ H, σ ⋆ τ) ≤ max{χ(G, σ), χ(H, τ) + 2(Δ(G) + 1)}. Then we study circular coloring of corona products of graphs, and obtained the following upper bounds: χc(G ⊙ H, σ ⊙ τ) ≤ max{χc(G, σ), χc(H, τ) + 4}, χc(G ⋄ H, σ ⋄ τ) ≤ max{χc(G, σ), χc(H, τ) + 8}, and χc(G ⋆ H, σ ⋆ τ) ≤ max{χc(G, σ), χc(H, τ) + 4(Δ(G) + 1)}. We shall show that the upper bound for the circular chromatic number of vertex corona product is attained, by constructing signed Paley graph that achieves this upper bound.
Characterizations on the hop Roman domination in trees Elahe Shabani; Nader Jafari Rad; Abolfazl Poureidi
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 14, No 2 (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.2026.14.2.10

Abstract

A subset S of vertices of G is a hop dominating set if every vertex outside S is at distance two from a vertex of S. The hop domination number of G, denoted by γh(G), is the minimum cardinality of a hop dominating set of G. A hop Roman dominating function (HRDF) of G is a function f : V(G) ⟶ {0, 1, 2} having the property that for every vertex v ∈ V with f(v) = 0 there is a vertex u with f(u) = 2 and d(u, v) = 2. The weight of a HRDF f is the sum f(V) = ∑v∈Vf(v). The minimum weight of HRDF on G is called the hop Roman domination number of G, and is denoted by γhR(G). In this paper we characterize all graphs G with γhR(G) = γh(G), all trees T for which γhR(T) = γh(T) + 1 as well as all trees T for which γhR(T) = γh(T) + 2.
Some algebraic invariants of ideals associated with graph families Hafsa Bibi; Hanni Garminia; . Irawati; Asia Rauf; Um- E- Aimen
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 14, No 2 (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.2026.14.2.5

Abstract

In this article, we study some algebraic invariants of monomial ideals associated with graphs. Specifically, we compute the depth and Stanley depth of edge ideals arising from sunlet graphs, cycle-related graphs, and wheel-related graphs. In addition, we show that the path ideal of length two in centipede-related graphs satisfies both the persistence and strong persistence properties.
On (a, d)-distance antimagic labeling of 2-regular graphs containing 6-cycles Muhammad Husnul Khuluq; Anak Agung Gede Ngurah; Noor Hidayat; Vira Hari Krisnawati
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 14, No 2 (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

Abstract

A graph G = (V(G), E(G)) of order n is called (a, d)-distance antimagic if there exists a bijection ℓ : V(G) → {1, 2, …, n} such that the set of vertex weights is {a, a + d, a + 2d, …, a + (n − 1)d}, where a > 0 and d ≥ 0. In such a case, ℓ is called an (a, d)-distance antimagic labeling of G. In this paper, we provide necessary and sufficient conditions of the graphs Cn ∪ tC6 where n ∈ {5, 7, 9, 11}, C2t+1 ∪ tC6, m(Cn ∪ C6), mCn ∪ ½(mn − 1)C6, and C10 ∪ mC3 ∪ tC6 to be (a, d)-distance antimagic for some positive integers m, n, and t.
Injective edge-coloring of claw-free graphs with maximum degree 4 Danjun Huang; Yuqian Guo
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 14, No 2 (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.2026.14.2.6

Abstract

An injective k-edge-coloring of a graph G is a mapping ϕ : E(G) → {1, 2, …, k}, such that ϕ(e) ≠ ϕ(e′) if edges e and e′ are at distance two, or are in a triangle. The smallest integer k such that G has an injective k-edge-coloring is called the injective chromatic index of G, denoted by χ′i(G). A graph is called claw-free if it has no induced subgraph isomorphic to the complete bipartite graph K1,3. In this paper, we show that χ′i(G) ≤ 13 for every claw-free graph G with Δ(G) ≤ 4, where Δ(G) is the maximum degree of G.
Spectral properties of mixed radial Moore graphs J.M. Ceresuela; Cristina Dalfó; M.A. Fiol; Nacho López; J.M. Miret
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 14, No 2 (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.2026.14.2.12

Abstract

The pioneering study of Moore graphs by Hoffman and Singleton exploits the properties of the eigenvalues of the adjacency matrix of graphs. Radial Moore graphs are extremal graphs related to the Moore ones, where the distance-preserving spanning tree is preserved for some vertices. In this paper, we present some equations involving the adjacency matrix of a mixed radial Moore graph. These equations are used as a basis to create some spectral measures that lead us to rank mixed radial Moore graphs and show which graph is the closest graph to being a mixed Moore graph.
Upper bounds of the strong 3-rainbow index of corona product graphs M Salman A.N.; Zata Yumni Awanis; Suhadi Wido Saputro
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 14, No 2 (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.2026.14.2.1

Abstract

A tree in an edge-colored connected graph G of order n, where adjacent edges may be colored the same, is a rainbow tree if no two of its edges have the same color. Let k be an integer with 2 ≤ k ≤ n. An edge-coloring of G is called a strong k-rainbow coloring of G if for every S ⊆ V(G) with |S| = k, there exists a rainbow tree of minimum size connecting S. The minimum number of colors that are needed such that G admits a strong k-rainbow coloring is called the strong k-rainbow index of G, denoted by srxk(G). In this paper, we study the srx3 of corona product between two connected graphs G and H, denoted by G ⊙ H. We first provide an algorithm to define a strong 3-rainbow coloring of G ⊙ H. Hence, we obtain a sharp upper bound for srx3(G ⊙ H). We also characterize graphs H with srx3(Tn ⊙ H) equals the upper bound.

Page 41 of 42 | Total Record : 413

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