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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 12 Documents
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Search results for , issue "Vol 12, No 1 (2024): Electronic Journal of Graph Theory and Applications" : 12 Documents clear
On 14-regular distance magic graphs Kovář, Petr; Krbeček, Matěj
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.2024.12.1.4

Abstract

Let G be a graph with n vertices. By N(v) we denote the set of all vertices adjacent to v. A bijection f : V(G)→{1, 2, …, n} is a distance magic labeling of G if there exists an integer k such that the sum of labels of all vertices adjacent to v is k for all vertices v in V(G). A graph which admits a distance magic labeling is a distance magic graph. In this paper, we completely characterize all orders for which a 14-regular distance magic graph exists. Hereby we extended similar results on 2-, 4-, 6-, 8-, 10-, and 12-regular distance magic graphs.
The dispersability of the Kronecker cover of the product of complete graphs and cycles Shao, Zeling; Cui, Yaqin; Li, Zhiguo
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.2024.12.1.10

Abstract

The Kronecker cover of a graph G is the Kronecker product of G and K2. The matching book embedding of a graph G is an embedding of G with the vertices on the spine, each edge within a single page so that the edges on each page do not intersect and the degree of vertices on each page is at most one. The matching book thickness of G is the minimum number of pages in a matching book embeddding of G and it denoted by mbt(G). A graph G is dispersable if mbt(G)=Δ(G), nearly dispersable if mbt(G)=Δ(G)+1. In this paper, the dispersability of the Kronecker cover of the Cartesian product of complete graphs Kp and cycles Cq is determined.
Forbidden family of Ph-magic graphs Maryati, Tita Khalis; Hadiputra, Fawwaz Fakhrurrozi; Salman, A. N. 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.2024.12.1.5

Abstract

Let G be a simple, finite, and undirected graph and H be a subgraph of G. The graph G admits an H-covering if every edge in G belongs to a subgraph isomorphic to H. A bijection f : V(G)∪E(G)→[1, n] is a magic total labeling if for every subgraphs H′ isomorphic to H, the sum of labels of all vertices and edges in H′ is constant. If there exists such f, we say G is H-magic. A graph F is said to be a forbidden subgraph of H-magic graphs if F ⊆ G implies G is not an H-magic graph. A set that contains all forbidden subgraph of H-magic is called forbidden family of H-magic graphs, denoted by F(H). In this paper, we consider F(Ph), where Ph is a path of order h. We present some sufficient conditions of a graph being a member of F(Ph). Besides that, we show the uniqueness of a minimal tree which belongs to F(P3) and characterize P3-(super)magic trees.
The local metric dimension of amalgamation of graphs Fitriani, Dinny; Saputro, Suhadi Wido
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.2024.12.1.11

Abstract

For any two adjacent vertices u and v in graph G, a set of vertices W locally resolves a graph G if the distance of u and v to some elements of W are distinct. The local metric dimension of G is the minimum cardinality of local resolving sets of G. For n ∈ N and i ∈ {1, 2, …, n}, let Hi be a simple connected graph containing a connected subgraph J. Let H = {H1, H2, …, Hn} be a finite collection of simple connected graphs. The subgraph-amalgamation of H = {H1, H2, …, Hn}, denoted by Subgraph − Amal{H; J}, is a graph obtained by identifying all elements of H in J. The subgraph J is called as a terminal subgraph of H. In this paper, we determine general bounds of the local metric dimension of subgraph-amalgamation graphs for any connected terminal subgraphs. We also determine the local metric dimension of Subgraph − Amal{H; J} for J is either K1 or P2.
Edge-locating coloring of graphs Korivand, Meysam; Mojdeh, Doost Ali; Baskoro, Edy Tri; Erfanian, Ahmad
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.2024.12.1.6

Abstract

An edge-locating coloring of a simple connected graph G is a partition of its edge set into matchings such that the vertices of G are distinguished by the distance to the matchings. The minimum number of the matchings of G that admits an edge-locating coloring is the edge-locating chromatic number of G, and denoted by χ′L(G). This paper introduces and studies the concept of edge-locating coloring. Graphs G with χ′L(G)∈{2, m} are characterized, where m is the size of G. We investigate the relationship between order, diameter and edge-locating chromatic number. We obtain the exact values of χ′L(Kn) and χ′L(Kn − M), where M is a maximum matching; indeed this result is also extended for any graph. We determine the edge-locating chromatic number of the join graphs of some well-known graphs. In particular, for any graph G, we show a relationship between χ′L(G + K1) and Δ(G). We investigate the edge-locating chromatic number of trees and present a characterization bound for any tree in terms of maximum degree, number of leaves, and the support vertices of trees. Finally, we prove that any edge-locating coloring of a graph is an edge distinguishing coloring.
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.

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