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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 the non-commuting graph of dihedral group Sanhan Muhammad Salih Khasraw; Ivan Dler Ali; Rashad Rashid Haji
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.2020.8.2.3

Abstract

For a nonabelian group G, the non-commuting graph Γ of G is defined as the graph with vertex-set G-Z(G), where Z(G) is the center of G, and two distinct vertices of Γ are adjacent if they do not commute in G. In this paper, we investigate the detour index, eccentric connectivity and total eccentricity polynomials of the non-commuting graph on D2n. We also find the mean distance of the non-commuting graph on D2n.
On open neighborhood locating-dominating in graphs Mustapha Chellali; Nader Jafari Rad; Suk Jai Seo; Peter James Slater
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.2014.2.2.1

Abstract

A set D of vertices in a graph G = (V (G), E(G)) is an open neighborhood locating-dominating set (OLD-set) for G if for every two vertices u, v of V (G) the sets N(u) ∩ D and N(v) ∩ D are non-empty and different. The open neighborhood locating-dominating number OLD(G) is the minimum cardinality of an OLD-set for G. In this paper we characterize graphs G of order n with OLD(G) = 2, 3, or n and graphs with minimum degree (G) ≥ 2 that are C4-free with OLD(G) = n-1.
Restricted size Ramsey number for path of order three versus graph of order five Denny Riama Silaban; Edy Tri Baskoro; Saladin Uttunggadewa
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.2017.5.1.15

Abstract

Let $G$ and $H$ be simple graphs. The Ramsey number for a pair of graph $G$ and $H$ is the smallest number $r$ such that any red-blue coloring of edges of $K_r$ contains a red subgraph $G$ or a blue subgraph $H$. The size Ramsey number for a pair of graph $G$ and $H$ is the smallest number $\hat{r}$ such that there exists a graph $F$ with size $\hat{r}$ satisfying the property that any red-blue coloring of edges of $F$ contains a red subgraph $G$ or a blue subgraph $H$. Additionally, if the order of $F$ in the size Ramsey number is $r(G,H)$, then it is called the restricted size Ramsey number. In 1983, Harary and Miller started to find the (restricted) size Ramsey number for any pair of small graphs with order at most four. Faudree and Sheehan (1983) continued Harary and Miller's works and summarized the complete results on the (restricted) size Ramsey number for any pair of small graphs with order at most four. In 1998, Lortz and Mengenser gave both the size Ramsey number and the restricted size Ramsey number for any pair of small forests with order at most five. To continue their works, we investigate the restricted size Ramsey number for a path of order three versus connected graph of order five.
Decomposition of complete graphs into connected bipartite unicyclic graphs with eight edges John Fahnenstiel; Dalibor Froncek
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.2019.7.2.4

Abstract

We prove that each of the 34 non-isomorphic connected unicyclic bipartite graphs with eight edges decomposes the complete graph Kn whenever the necesary conditions are satisfied.
Chromatically unique 6-bridge graph theta(a,a,a,b,b,c) N.S.A. Karim; Roslan Hasni; Gee-Choon Lau
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.2016.4.1.6

Abstract

For a graph $G$, let $P(G,\lambda)$ denote the chromatic polynomial of $G$. Two graphs $G$ and $H$ are chromatically equivalent if they share the same chromatic polynomial. A graph $G$ is chromatically unique if for any graph chromatically equivalent to $G$ is isomorphic to $G$. In this paper, the chromatically unique of a new family of 6-bridge graph $\theta(a,a,a,b,b,c)$ where $2\le a\le b\le c$ is investigated.
Total vertex irregularity strength of trees with maximum degree five S. Susilawati; Edy Tri Baskoro; Rinovia Simanjuntak
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.2018.6.2.5

Abstract

In 2010, Nurdin, Baskoro, Salman and Gaos conjectured that the total vertex irregularity strength of any tree T is determined only by the number of vertices of degrees 1, 2 and 3 in T. This paper will confirm this conjecture by considering all trees with maximum degree five. Furthermore, we also characterize all such trees having the total vertex irregularity strength either t1, t2 or t3, where $t_{i} = \lceil (1+\sum\sb{j=1}\sp{i}n_{j})/(i+1)\rceil$ and ni is the number of vertices of degree i.
Some structural graph properties of the non-commuting graph of a class of finite Moufang loops Hamideh Hasanzadeh Bashir; Karim Ahmadidelir
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.2020.8.2.9

Abstract

For any non-abelian group G, the non-commuting graph of G, Γ=ΓG, is a graph with vertex set G \ Z(G), where Z(G) is the set of elements of G that commute with every element of G and distinct non-central elements x and y of G are joined by an edge if and only if xy ≠ yx. This graph is connected for a non-abelian finite group and has received some attention in existing literature. Similarly, the non-commuting graph of a finite Moufang loop has been defined by Ahmadidelir. He has shown that this graph is connected (as for groups) and obtained some results related to the non-commuting graph of a finite non-commutative Moufang loop. In this paper, we show that the multiple complete split-like graphs are perfect (but not chordal) and deduce that the non-commuting graph of Chein loops of the form M(D2n,2) is perfect but not chordal. Then, we show that the non-commuting graph of a non-abelian group G  is split if and only if the non-commuting graph of the Moufang loop M(G,2) is 3-split and then classify all Chein loops that their non-commuting graphs are 3-split. Precisely, we show that for a  non-abelian group G, the non-commuting graph of the Moufang loop M(G,2), is 3-split if and only if G is isomorphic to a Frobenius group of order 2n, n is odd, whose Frobenius kernel is abelian of order n. Finally, we calculate the energy  of  generalized and multiple splite-like graphs, and discuss about the energy and also the number of spanning trees in the case of  the non-commuting graph of  Chein loops of the form M(D2n,2).
On k-geodetic digraphs with excess one Anita Abildgaard Sillasen
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.2014.2.2.7

Abstract

A k-geodetic digraph G is a digraph in which, for every pair of vertices u and v (not necessarily distinct), there is at most one walk of length at most k from u to v. If the diameter of G is k, we say that G is strongly geodetic. Let N(d,k) be the smallest possible order for a k-geodetic digraph of minimum out-degree d, then N(d,k) is at most 1+d+d^2+...+d^k=M(d,k), where M(d,k) is the Moore bound obtained if and only if G is strongly geodetic. Thus strongly geodetic digraphs only exist for d=1 or k=1, hence for d,k >1 we wish to determine if N(d,k)=M(d,k)+1 is possible. A k-geodetic digraph with minimum out-degree d and order M(d,k)+1 is denoted as a (d,k,1)-digraph or said to have excess 1.In this paper we will prove that a (d,k,1)-digraph is always out-regular and that if it is not in-regular, then it must have 2 vertices of in-degree less than d, d vertices of in-degree d+1 and the remaining vertices will have in-degree d.Furthermore we will prove there exist no (2,2,1)-digraphs and no diregular (2,k,1)-digraphs for k> 2.
"Transit data"-based MST computation Thodoris Karatasos; Evi Papaioannou
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 5, No 2 (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.2017.5.2.6

Abstract

In this work, we present an innovative image recognition technique which is based on the exploitation of transit-data in images or simple photographs of sites of interest. Our objective is to automatically transform real-world images to graphs and, then, compute Minimum Spanning Trees (MST) in them.We apply this framework and present an application which automatically computes efficient construction plans (for escalator or low-emission hot spots) for connecting all points of interest in cultural sites, i.e., archaeological sites, museums, galleries, etc, aiming to to facilitate global physical access to cultural heritage and artistic work and make it accessible to all groups of population.
Exponent-critical primitive graphs and the Kronecker product Olga O'Mahony; Rachel Quinlan
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.2019.7.2.10

Abstract

A directed graph is primitive of exponent t if it contains walks of length t between all pairs of vertices, and t is minimal with this property. Moreover, it is exponent-critical if the deletion of any arc results in an imprimitive graph or in a primitive graph with strictly greater exponent. We establish necessary and sufficient conditions for the Kronecker product of a pair of graphs to be exponent-critical of prescribed exponent, defining some refinements of the concept of exponent-criticality in the process.

Page 8 of 39 | Total Record : 382

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