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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 382 Documents
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On normalized Laplacian spectrum of zero divisor graphs of commutative ring ℤn S. Pirzada; Bilal A. Rather; T. A. Chishti; U. Samee
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 9, No 2 (2021): 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.2021.9.2.7

Abstract

For a finite commutative ring ℤn with identity 1 ≠ 0, the zero divisor graph Γ(ℤn) is a simple connected graph having vertex set as the set of non-zero zero divisors, where two vertices x and y are adjacent if and only if xy=0. We find the normalized Laplacian spectrum of the zero divisor graphs Γ(ℤn) for various values of n and characterize n for which Γ(ℤn) is normalized Laplacian integral. We also obtain bounds for the sum of graph invariant Sβ*(G)-the sum of the β-th power of the non-zero normalized Laplacian eigenvalues of Γ(ℤn).
Edge erasures and chordal graphs Jared Culbertson; Dan P. Guralnik; Peter F. Stiller
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 9, No 2 (2021): 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.2021.9.2.13

Abstract

We prove several results about chordal graphs and weighted chordal graphs by focusing on exposed edges. These are edges that are properly contained in a single maximal complete subgraph.  This leads to a characterization of chordal graphs via deletions of a sequence of exposed edges from a complete graph. Most interesting is that in this context the connected components of the edge-induced subgraph of exposed edges are 2-edge connected.  We use this latter fact in the weighted case to give a modified version of Kruskal's second algorithm for finding a minimum spanning tree in a weighted chordal graph.  This modified algorithm benefits from being local in an important sense.
Chromatic number of super vertex local antimagic total labelings of graphs Fawwaz F. Hadiputra; Kiki A. Sugeng; Denny R. Silaban; Tita K. Maryati; Dalibor Froncek
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 9, No 2 (2021): 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.2021.9.2.19

Abstract

Let G(V,E) be a simple graph and f be a bijection f : V ∪ E → {1, 2, …, |V|+|E|} where f(V)={1, 2, …, |V|}. For a vertex x ∈ V, define its weight w(x) as the sum of labels of all edges incident with x and the vertex label itself. Then f is called a super vertex local antimagic total (SLAT) labeling if for every two adjacent vertices their weights are different. The super vertex local antimagic total chromatic number χslat(G) is the minimum number of colors taken over all colorings induced by super vertex local antimagic total labelings of G. We classify all trees T that have χslat(T)=2, present a class of trees that have χslat(T)=3, and show that for any positive integer n ≥ 2 there is a tree T with χslat(T)=n.
Evaluating topological ordering in directed acyclic graphs Suzana Antunović; Damir Vukičević
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 9, No 2 (2021): 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.2021.9.2.25

Abstract

Directed acyclic graphs are often used to model situations and problems in real life. If we consider the topological ordering of the graph as a process of arranging the vertices in the best possible way considering the constraints caused by the direction of edges, then it makes sense to try to optimize this process by minimizing the distances between vertices in the ordering. For this purpose, we define measures based on distances between vertices in the topological ordering that allow us to construct a graph with optimal topological ordering regarding a specific measure thus minimizing the complexity of the system represented by the graph. We explore minimal and maximal values of the defined measures and comment on the topology of graphs for which maximal and minimal values are obtained. Potentially, the proved bounds could be used to benchmark existing algorithms, devise new approximation algorithms or branch and bound schemas for some scheduling problems that are usually of hard computational complexity.
Lower bounds for the algebraic connectivity of graphs with specified subgraphs Zoran Stanic
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 9, No 2 (2021): 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.2021.9.2.2

Abstract

The second smallest eigenvalue of the Laplacian matrix of a graph G is called the algebraic connectivity and denoted by a(G). We prove thata(G)>π2/3(p(12g(n1, n2, …, np)2 − π2)/4g(n1, n2, …, np)4 + 4(q − p)(3g(np + 1, np + 2, …, nq)2 − π2)/g(np + 1, np + 2, …, nq)4),holds for every non-trivial graph G which contains edge-disjoint spanning subgraphs G1, G2, …,  Gq such that, for 1 ≤ i ≤ p, a(Gi)≥a(Pni), with ni ≥ 2, and, for p + 1 ≤ i ≤ q, a(Gi)≥a(Cni), where Pni and Cni denote the path and the cycle of the corresponding order, respectively, and g denotes the geometric mean of given arguments. Among certain consequences, we emphasize the following lower bounda(G)>π212(4q − 3p)n2 − (16q − 15p)π2/12n4,referring to G which has n (n ≥ 2) vertices and contains p Hamiltonian paths and q − p Hamiltonian cycles, such that all of them are edge-disjoint. We also discuss the quality of the obtained lower bounds.
Odd facial colorings of acyclic plane graphs Július Czap; Peter Šugerek
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 9, No 2 (2021): 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.2021.9.2.8

Abstract

Let G be a connected plane graph with vertex set V and edge set E. For X ∈ {V, E, V ∪ E}, two elements of X are facially adjacent in G if they are incident elements, adjacent vertices, or facially adjacent edges (edges that are consecutive on the boundary walk of a face of G). A coloring of G is facial with respect to X if there is a coloring of elements of X such that facially adjacent elements of X receive different colors. A facial coloring of G is odd if for every face f and every color c, either no element or an odd number of elements incident with f is colored by c. In this paper we investigate odd facial colorings of trees. The main results of this paper are the following: (i) Every tree admits an odd facial vertex-coloring with at most 4 colors; (ii) Only one tree needs 6 colors, the other trees admit an odd facial edge-coloring with at most 5 colors; and (iii) Every tree admits an odd facial total-coloring with at most 5 colors. Moreover, all these bounds are tight.
Tarantula graphs are determined by their Laplacian spectrum Reza Sharafdini; Ali Zeydi Abdian
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 9, No 2 (2021): 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.2021.9.2.14

Abstract

A graph G is said to be determined by its Laplacian spectrum (DLS) if every graph with the same Laplacian spectrum is isomorphic to G. A graph which is a collection of hexagons (lengths of these cycles can be different) all sharing precisely one vertex is called a spinner graph. A tree with exactly one vertex of degree greater than 2 is called a starlike tree. If a spinner graph and a starlike tree are joined by merging their vertices of degree greater than 2, then the resulting graph is called a tarantula graph. It is known that spinner graphs and starlike trees are DLS.  In this paper, we prove that tarantula graphs are determined by their Laplacian spectrum.
Representing non-crossing cuts by phylogenetic trees Thomas Lange
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 9, No 2 (2021): 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.2021.9.2.20

Abstract

Phylogenetic trees are representations of the evolutionary descendency of a set of species. In graph-theoretic terms, a phylogenetic tree is a partially labeled tree where unlabeled vertices have at least degree three and labels corresponds to pairwise disjoint subsets of the set of species. A cut of a graph G = (V, E) is defined as bipartition {S, V \ S} of the vertex set V of G. A pair of cuts {S, S}, {T, T} is said to be crossing, if neither S ∩ T, S ∩ T, S ∩ T nor S ∩ T is empty. In this paper, we show that each set of pairwise non-crossing cuts of a graph G can be represented uniquely by a phylogenetic tree such that the set of species corresponds to the vertex set of G.
On n-connected minors of the es-splitting binary matroids Prashant Pralhad Malavadkar; Santosh Baburao Dhotre; Maruti Shikare
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 9, No 2 (2021): 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.2021.9.2.3

Abstract

The es-splitting operation on an n-connected binary matroid may not yield an n-connected matroid for (n ≥ 3). In this paper, we show that given an n-connected binary matroid M of rank r, the resulting es-splitting binary matroid has an n-connected minor of rank-(r + 1) having |E(M)| + 1 elements.
Multicolor star-critical Ramsey numbers and Ramsey-good graphs Mark Rowland Budden; Elijah DeJonge
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 10, No 1 (2022): 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.2022.10.1.4

Abstract

This paper seeks to develop the multicolor version of star-critical Ramsey numbers, which serve as a measure of the strength of the corresponding Ramsey numbers.  We offer several general theorems, some of which focus on Ramsey-good cases (i.e., cases in which the corresponding Ramsey number is equal to a general lower bound).  We also prove some specific cases for small graphs, and conclude with a table of known multicolor star-critical Ramsey numbers.

Page 24 of 39 | Total Record : 382

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