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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
 1   2   3   4   5 
On a directed tree problem motivated by a newly introduced graph product Antoon H. Boode; Hajo Broersma; Jan F. Broenink
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 3, No 2 (2015): 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.2015.3.2.5

Abstract

In this paper we introduce and study a directed tree problem motivated by a new graph product that we have recently introduced and analysed in two conference contributions in the context of periodic real-time processes. While the two conference papers were focussing more on the applications, here we mainly deal with the graph theoretical and computational complexity issues. We show that the directed tree problem is NP-complete and present and compare several heuristics for this problem.
New bounds on the hyper-Zagreb index for the simple connected graphs Suresh Elumalai; Toufik Mansour; Mohammad Ali Rostami
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 6, No 1 (2018): 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.2018.6.1.12

Abstract

The hyper-Zagreb index of a simple connected graph G is defined by χ2(G) = ∑uv ∈ E(G)(d(u) + d(v))2. In this paper, we establish, analyze and compare some new upper bounds on the Hyper-Zagreb index in terms of the number of vertices n, number of edges m, maximum vertex degree Δ, and minimum vertex degree δ, first Zagreb index M1(G), second Zagreb index M2(G), harmonic index H(G), and inverse edge degree IED(G). In addition, we give the identities on Hyper-Zagreb index and its coindex for the simple connected graphs.
16-vertex graphs with automorphism groups A4 and A5 from the icosahedron Peteris Daugulis
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 8, No 2 (2020): 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.2020.8.2.1

Abstract

The article deals with the problem of finding vertex-minimal graphs with a given automorphism group. We exhibit two undirected 16-vertex graphs having automorphism groups A4 and A5. It improves Babai's bound for A4 and the graphical regular representation bound for A5. The graphs are constructed using projectivisation of the vertex-face graph of the icosahedron. 
The Ramsey numbers of fans versus a complete graph of order five Yanbo Zhang; Yaojun Chen
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 2, No 1 (2014): 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.2014.2.1.6

Abstract

For two given graphs $F$ and $H$, the Ramsey number $R(F,H)$ is the smallest integer $N$ such that for any graph $G$ of order $N$, either $G$ contains $F$ or the complement of $G$ contains $H$. Let $F_l$ denote a fan of order $2l+1$, which is $l$ triangles sharing exactly one vertex, and $K_n$ a complete graph of order $n$. Surahmat et al. conjectured that $R(F_l,K_n)=2l(n-1)+1$ for $l\geq n\geq 5$. In this paper, we show that the conjecture is true for n=5.
Traversing every edge in each direction once, but not at once: Cubic (polyhedral) graphs Vladimir R. Rosenfeld
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 5, No 1 (2017): 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.2017.5.1.13

Abstract

A {\em retracting-free bidirectional circuit} in a graph $G$ is a closed walk which traverses every edge exactly once in each direction and such that no edge is succeeded by the same edge in the opposite direction. Such a circuit revisits each vertex only in a number of steps. Studying the class $\mathit{\Omega}$ of all graphs admitting at least one retracting-free bidirectional circuit was proposed by Ore (1951) and is by now of practical use to nanotechnology. The latter needs in various molecular polyhedra that are constructed from a single chain molecule in the retracting-free way. Some earlier results for simple graphs, obtained by Thomassen and, then, by other authors, are specially refined by us for a cubic graph $Q$. Most of such refinements depend only on the number $n$ of vertices of $Q$.
Note on chromatic polynomials of the threshold graphs Noureddine Chikh; Miloud Mihoubi
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 7, No 2 (2019): 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.2019.7.2.2

Abstract

Let G be a threshold graph. In this paper, we give, in first hand, a formula relating the chromatic polynomial of Ḡ (the complement of G) to the chromatic polynomial of G. In second hand, we express the chromatic polynomials of G and Ḡ in terms of the generalized Bell polynomials.
A graph theoretical analysis of the number of edges in k-dense graphs Linda Eroh; Henry Escuadro; Ralucca Gera; Samuel Prahlow; Karl Schmitt
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 4, No 1 (2016): 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.2016.4.1.4

Abstract

Due to the increasing discovery and implementation of networks within all disciplines of life, the study of subgraph connectivity has become increasingly important. Motivated by the idea of community (or subgraph) detection within a network/graph, we focused on finding characterizations of k-dense communities. For each edge $uv\in E(G)$, the {\bf edge multiplicity} of $uv$ in $G$ is given by $m_G(uv)=|N_{G}(u)\cap N_{G}(v)|.$ For an integer $k$ with $k\ge 2$, a {\bf $\boldsymbol{k}$-dense community} of a graph $G$, denoted by $DC_k(G)$, is a maximal connected subgraph of $G$ induced by the vertex set$V_{DC_k(G)} = \{v\in V(G) : \exists u\in V(G)\ {\rm such\ that\ } uv\in E(G)\ {\rm and\ } m_{DC_{k(G)}}(uv)\ge k-2\}.$In this research, we characterize which graphs are $k$-dense but not $(k+1)$-dense for some values of $k$ and study the minimum and maximum number of edges such graphs can have. A better understanding of $k$-dense sub-graphs (or communities) helps in the study of the connectivity of large complex graphs (or networks) in the real world.
Domination number of the non-commuting graph of finite groups Ebrahim Vatandoost; Masoumeh Khalili
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 6, No 2 (2018): 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.2018.6.2.3

Abstract

Let G be a non-abelian group. The non-commuting graph of group G, shown by ΓG, is a graph with the vertex set G \ Z(G), where Z(G) is the center of group G. Also two distinct vertices of a and b are adjacent whenever ab ≠ ba. A set S ⊆ V(Γ) of vertices in a graph Γ is a dominating set if every vertex v ∈ V(Γ) is an element of S or adjacent to an element of S. The domination number of a graph Γ denoted by γ(Γ), is the minimum size of a dominating set of Γ. </p><p>Here, we study some properties of the non-commuting graph of some finite groups. In this paper, we show that $\gamma(\Gamma_G)&lt;\frac{|G|-|Z(G)|}{2}.$ Also we charactrize all of groups G of order n with t = ∣Z(G)∣, in which $\gamma(\Gamma_{G})+\gamma(\overline{\Gamma}_{G})\in \{n-t+1,n-t,n-t-1,n-t-2\}.$
Uniform edge betweenness centrality Heather Newman; Hector Miranda; Rigoberto Flórez; Darren A Narayan
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 8, No 2 (2020): 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.2020.8.2.7

Abstract

The edge betweenness centrality of an edge is loosely defined as the fraction of shortest paths between all pairs of vertices passing through that edge. In this paper, we investigate graphs where the edge betweenness centrality of edges is uniform. It is clear that if a graph G is edge-transitive (its automorphism group acts transitively on its edges) then G has uniform edge betweenness centrality. However this sufficient condition is not necessary. Graphs that are not edge-transitive but have uniform edge betweenness centrality appear to be very rare. Of the over 11.9 million connected graphs on up to ten vertices, there are only four graphs that are not edge-transitive but have uniform edge betweenness centrality. Despite this rarity among small graphs, we present methods for creating infinite classes of graphs with this unusual combination of properties. 
Fibonacci number of the tadpole graph Joe DeMaio; John Jacobson
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 2, No 2 (2014): 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.2014.2.2.5

Abstract

In 1982, Prodinger and Tichy defined the Fibonacci number of a graph G to be the number of independent sets of the graph G. They did so since the Fibonacci number of the path graph Pn is the Fibonacci number F(n+2) and the Fibonacci number of the cycle graph Cn is the Lucas number Ln. The tadpole graph Tn,k is the graph created by concatenating Cn and Pk with an edge from any vertex of Cn to a pendant of Pk for integers n=3 and k=0. This paper establishes formulae and identities for the Fibonacci number of the tadpole graph via algebraic and combinatorial methods.

Page 1 of 39 | Total Record : 382

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