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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 15 Documents
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Search results for , issue "Vol 12, No 2 (2024): Electronic Journal of Graph Theory and Applications" : 15 Documents clear
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.
The real equiangular tight frames obtained from rank 3 graphs Bannai, Eiichi; Bannai, Etsuko; Lee, Chin-Yen; Tanaka, Hajime; Yu, Wei-Hsuan
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.2024.12.2.12

Abstract

We present all nontrivial real equiangular tight frames {φm}m=1M in RN obtained as spherical embeddings of primitive rank 3 graphs on M vertices, and those such that one of their associated M strongly regular graphs on M - 1 vertices is a primitive rank 3 graph.
Determination of all graphs whose eccentric graphs are clusters Akiyama, Jin; Kodate, Takako; Matsunaga, Kiyoko
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.2024.12.2.1

Abstract

A disconnected graph G is called a cluster if G is not union of K2s (1-factor) but union of complete graphs of order at least two. J. Akiyama, K. Ando and D. Avis showed in Lemma 2.1 of [2] that G is equi-eccentric if the eccentric graph Ge is a cluster or pK2. And they also characterized all graphs whose eccentric graphs are complete graphs and pK2 in [2]. In this paper, we determined in Theorem 2 all graphs whose eccentric graphs are clusters, which is an extension of Lemma 2.1 in [2].  
Partition dimension of trees - palm approach Hafidh, Yusuf; Baskoro, Edy Tri
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.2024.12.2.7

Abstract

The partition dimension of a graph is the minimum number of vertex partitions such that every vertex has different distances to the ordered partitions. Many resolving partitions for trees have all vertices not in an end-path in the same partition. This reduces the problem of the partition dimension of trees into finding the partition dimension of palms, the end-paths from a branch. In this paper, we construct a resolving partition for trees using resolving partitions of their palms. We also study some bounds for the partition dimension of palms and also find the partition dimension of regular palm and olive trees.
Bounds for neighbor connectivity of Cayley graphs generated by trees and unicyclic graphs Abdallah, Mohamad
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.2024.12.2.13

Abstract

The neighbor connectivity refers to the minimum number of vertices whose removal, along with their neighbors, causes a previously connected graph to become disconnected. In this paper we focus on Cayley graphs constructed from the symmetric group Sn. We investigate the bounds of the neighbor connectivity for two cases: when the generating graph is a tree, and when it is a unicyclic graph with a unique cycle of length m, specifically considering cases where m = 3, m = n - 1, or m = n.
On domination numbers of zero-divisor graphs of commutative rings Anderson, Sarah E.; Axtell, Mike; Kroschel, Brenda K.; Stickles, Jr., Joe A.
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.2024.12.2.2

Abstract

Zero-divisor graphs of a commutative ring R, denoted Γ(R), are well-represented in the literature. In this paper, we consider domination numbers of zero-divisor graphs. For reduced rings, Vatandoost and Ramezani characterized the possible graphs for Γ(R) when the sum of the domination numbers of Γ(R) and the complement of Γ(R) is n - 1, n, and n + 1, where n is the number of nonzero zero-divisors of R. We extend their results to nonreduced rings, determine which graphs are realizable as zero-divisor graphs, and provide the rings that yield these graphs.
1-well-covered graphs containing a clique of size n∕3 Deniz, Zakir
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.2024.12.2.8

Abstract

A graph is well-covered if all of its maximal independent sets have the same size. A graph that remains well-covered upon the removal of any vertex is called a 1-well-covered graph. These graphs, when they have no isolated vertices, are also known as W2 graphs. It is well-known that every graph G ∈ W2 has two disjoint maximum independent sets. In this paper, we investigate connected W2 graphs with n vertices that contain a clique of size n∕3. We prove that if the removal of two disjoint maximum independent sets from a graph G ∈ W2 leaves a clique of size at least 3, then G contains a clique of size n∕3. Using this result, we provide a complete characterization of these graphs, based on eleven graph families.
Rainbow connection number of corona product of graphs Septyanto, Fendy
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.2024.12.2.14

Abstract

In an edge-colored graph (where adjacent edges may have the same color), a rainbow path is a path whose edge colors are all distinct. The coloring is called a rainbow coloring if any two vertices can be connected by a rainbow path. The rainbow connection number rc(G) is the smallest number of colors in a rainbow coloring of G. The corona product G ∘ H of two graphs G and H is constructed from one copy of G and n = |V (G)| disjoint copies of H such that the i-th vertex of G is joined to all vertices in the i-th copy of H, for each i ∈{1,…,n}. Several resuls on the rainbow connection number of corona product have been published, but there are inaccuracies. In this paper, we close the gaps and add new results. The strong variant of rainbow connection number is also discussed.

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