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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 382 Documents
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A note on lower bounds for boxicity of graphs Kamibeppu, Akira
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 12, No 1 (2024): 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.2024.12.1.12

Abstract

The boxicity of a graph G is the minimum non-negative integer k such that G is isomorphic to the intersection graph of a family of boxes in Euclidean k-space, where a box in Euclidean k-space is the Cartesian product of k closed intervals on the real line. In this short note, we define the fractional boxicity of a graph as the optimum value of the linear relaxation of a covering problem with respect to boxicity, which gives a lower bound for its boxicity.  We show that the fractional boxicity of a graph is at least the lower bounds for boxicity given by Adiga et al. in 2014.  We also present a natural lower bound for fractional boxicity of graphs. The aim of this note is to discuss and focus on “accuracy” rather than “simplicity” of these lower bounds for boxicity as the next step in the work by Adiga et al. 
Properly even harmonious labeling of a union of stars Henderson, Zachary M.
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 12, No 1 (2024): 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.2024.12.1.1

Abstract

A function f is defined as an even harmonious labeling on a graph G with q edges if f : V(G)→{0, 1, …, 2q} is an injection and the induced function f* : E(G)→{0, 2, …, 2(q − 1)} defined by f*(uv)=f(u)+f(v) (mod2q) is bijective. A properly even harmonious labeling is an even harmonious labeling in which the codomain of f is {0, 1, …, 2q − 1}, and a strongly harmonious labeling is an even harmonious labeling that also satisfies the additional condition that for any two adjacent vertices with labels u and v, 0 < u + v ≤ 2q. In , Gallian and Schoenhard proved that Sn1 ∪ Sn2 ∪ … ∪ Snt is strongly even harmonious for n1 ≥ n2 ≥ … ≥ nt and t < n1/2 + 2. In this paper, we begin with the related question “When is the graph of k n-star components, G = kSn, properly even harmonious?" We conclude that kSn is properly even harmonious if and only if k is even or k is odd, k > 1, and n ≥ 2. We also conclude that Sn1 ∪ Sn2 ∪ … ∪ Snk is properly even harmonious when k ≥ 2, ni ≥ 2 for all i and give some additional results on combinations of star and banana graphs.
Distance magic labelling of Mycielskian graphs Pawar, Ravindra Kuber; Singh, Tarkeshwar
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 12, No 1 (2024): 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.2024.12.1.7

Abstract

A graph G = (V, E), where |V(G)| = n and |E(G)| = m is said to be a distance magic graph if there is a bijection f : V(G)→{1, 2, …, n} such that the vertex weight w(u)=∑v ∈ N(u)f(v)=k is constant and independent of u, where N(u) is an open neighborhood of the vertex u. The constant k is called a distance magic constant, the function f is called a distance magic labeling of the graph G and the graph which admits such a labeling is called a distance magic graph. In this paper, we present some results on distance magic labeling of Mycielskian graphs.
A refined Tur'an theorem Filipovski, Slobodan
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 12, No 1 (2024): 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.2024.12.1.2

Abstract

Let G = (V, E) be a finite undirected graph with vertex set V(G) of order |V(G)| = n and edge set E(G) of size |E(G)| = m. Let Δ = d1 ≥ d2 ≥ ⋯ ≥ dn = δ be the degree sequence of the graph G. A clique in a graph G is a complete subgraph of G. The clique number of a graph G, denoted by ω(G), is the order of a maximum clique of G. In 1907 Mantel proved that a triangle-free graph with n vertices can contain at most ⌊n2/4⌋ edges. In 1941 Tur'an generalized Mantel’s result to graphs not containing cliques of size r by proving that graphs of order n that contain no induced Kr have at most (1 − 1/r − 1)n2/2 edges. In this paper, we give new bounds for the maximum number of edges in a Kr-free graph G of order n, minimum degree δ, and maximum degree Δ. We show that, for the families of graphs having the above properties, our bounds are slightly better than the more general bounds of Tur'an.
Tetravalent non-normal Cayley graphs of order 5p^2 Khazaei, Soghra; Sharifi, Hesam
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 12, No 1 (2024): 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.2024.12.1.8

Abstract

In this paper, we explore connected Cayley graphs on non-abelian groups of order 5p2, where p is a prime greater than 5, and Sylow p-subgroup is cyclic with respect to tetravalent sets that encompass elements with different orders. We prove that these graphs are normal; however, they are not normal edge-transitive, arc-transitive, nor half-transitive. Additionally, we establish that the group is a 5-CI-group.
On D-distance (anti)magic labelings of shadow graph of some graphs Ngurah, Anak Agung Gede; Inayah, Nur; Musti, Mohamad Irvan Septiar
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 12, No 1 (2024): 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.2024.12.1.3

Abstract

Let G be a graph with vertex set V(G) and diameter diam(G). Let D ⊆ {0, 1, 2, 3, …, diam(G)} and φ : V(G)→{1, 2, 3, …, |V(G)|} be a bijection. The graph G is called D-distance magic, if  s ∈ ND(t)φ(s) is a constant for any vertex t ∈ V(G). The graph G is called (α, β)-D-distance antimagic, if { s ∈ ND(t)φ(s):t ∈ V(G)} is a set {α, α + β, α + 2β, …, α + (|V(G)| − 1)β}. In this paper, we study D-distance (anti)magic labelings of shadow graphs for D = {1}, {0, 1}, {2}, and {0, 2}.
Modular irregularity strength of dense graphs Suparta, I Nengah; Candiasa, Made; Prasancika, Kadek Wahyu; Baca, Martin
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 12, No 1 (2024): 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.2024.12.1.9

Abstract

We solve the open problem posed in Modular irregularity strength of graphs, Electron. J. Graph Theory and Appl. 8 (2020), 435–433, asking about the modular irregularity strength of the complete graph Kn for all n ≥ 3. Furthermore, we establish also the exact values of the modular irregularity strength of complete bipartite graphs Kn, n + t for any positive integer n and t = 0, 1, 2.
The Alon-Tarsi number of cupolarotundas and gyroelongated rotunda Li, Zhiguo; Gai, Yujia; Shao, Zeling
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 12, No 2 (2024): 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.2024.12.2.5

Abstract

The Alon-Tarsi number of a graph G is the smallest k so that there exists an orientation D of G with max outdegree k - 1 satisfying the number of even Eulerian subgraphs different from the number of odd Eulerian subgraphs. This paper is devoted to the study of the Alon-Tarsi number of cupolarotundas and gyroelongated rotunda.
Group vertex magicness of H-join and generalised friendship graph Balamoorthy, S.; Bharanedhar, S.V.
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 12, No 2 (2024): 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.2024.12.2.11

Abstract

In this paper, we consider A-vertex magic graphs, where A is a non-trivial Abelian group. We characterize Z-vertex magic graphs. We also explore the relation between the A-vertex magicness of a graph G and its reduced graph. In addition, we introduce a new type of labeling called A′-vertex magic labeling of graphs and characterize A-vertex magicness using A′-vertex magicness. We give a new procedure to embed any graph as an induced subgraph of an A-vertex magic graph and we construct infinite families of A-vertex magic graphs both of these procedure uses less number of vertices compared to the one given in (Sabeel et al. in Australas. J. Combin. 85(1) (2023), 49-60) and we also generalize some results proved in this paper. Finally we completely classify generalised friendship graph using A-vertex magicness and group vertex magicness.
Upper Broadcast Domination Number of Caterpillars with no Trunks Bouchouika, Sabrina; Bouchemakh, Isma; Sopena, Eric
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 12, No 2 (2024): 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.2024.12.2.6

Abstract

A broadcast on a graph G = (V,E) is a function f : V →{0,…,diam(G)} such that f(v) ≤ eG(v) for every vertex v ∈ V , where diam(G) denotes the diameter of G and eG(v) the eccentricity of v in G. Such a broadcast f is minimal if there does not exist any broadcast g≠f on G such that g(v) ≤ f(v) for all v ∈ V . The upper broadcast domination number of G is the maximum value of ∑ v∈V f(v) among all minimal broadcasts f on G for which each vertex of G is at distance at most f(v) from some vertex v with f(v) ≥ 1. In this paper, we study the minimal dominating broadcasts of caterpillars and give the exact value of the upper broadcast domination number of caterpillars with no trunks.

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