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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 some covering graphs of a graph Shariefuddin Pirzada; Hilal A Ganie; Merajuddin Siddique
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 4, No 2 (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.2016.4.2.2

Abstract

For a graph $G$ with vertex set $V(G)=\{v_1, v_2, \dots, v_n\}$, let $S$ be the covering set of $G$ having the maximum degree over all the minimum covering sets of $G$. Let $N_S[v]=\{u\in S : uv \in E(G) \}\cup \{v\}$ be the closed neighbourhood of the vertex $v$ with respect to $S.$ We define a square matrix $A_S(G)= (a_{ij}),$ by $a_{ij}=1,$ if $\left |N_S[v_i]\cap N_S[v_j] \right| \geq 1, i\neq j$ and 0, otherwise. The graph $G^S$ associated with the matrix $A_S(G)$ is called the maximum degree minimum covering graph (MDMC-graph) of the graph $G$. In this paper, we give conditions for the graph $G^S$ to be bipartite and Hamiltonian. Also we obtain a bound for the number of edges of the graph $G^S$ in terms of the structure of $G$. Further we obtain an upper bound for covering number (independence number) of $G^S$  in terms of the covering number (independence number) of $G$.
On topological integer additive set-labeling of star graphs Hafizh M. Radiapradana; Suhadi Wido Saputro; Erma Suwastika; Oki Neswan; Andrea Semanicova-Fenovcıkova
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.2018.6.2.13

Abstract

For integer k ≥ 2, let X = {0, 1, 2, …, k}. In this paper, we determine the order of a star graph K1, n of n + 1 vertices, such that K1, n admits a topological integer additive set-labeling (TIASL) with respect to a set X. We also give a condition for a star graph K1, n such that K1, n is not a TIASL-graph on set X.
On the restricted size Ramsey number for P3 versus dense connected graphs Denny Riama Silaban; Edy Tri Baskoro; Saladin Uttunggadewa
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.2020.8.2.14

Abstract

Let F, G and H be simple graphs. A graph F is said a (G,H)-arrowing graph if in any red-blue coloring of edges of F we can find a red G or a blue H. The size Ramsey number of G and H, ŕ(G,H), is the minimum size of F. If the order of F equals to the Ramsey number of G and H, r(G,H), then the minimum size of F is called the restricted size Ramsey number of G and H, r*(G,H). The Ramsey number of G and H, r(G,H), is the minimum order of F. In this paper, we study the restricted size number involving a P3.  The value of r*(P3,Kn) has been given by Faudree and Sheehan. Here, we examine r*(P3,H) where H is dense connected graph.
Polynomial reconstruction of the matching polynomial Xueliang Li; Yongtang Shi; Martin Trinks
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 3, No 1 (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.2015.3.1.4

Abstract

The matching polynomial of a graph is the generating function of the numbers of its matchings with respect to their cardinality. A graph polynomial is polynomial reconstructible, if its value for a graph can be determined from its values for the vertex-deleted subgraphs of the same graph. This note discusses the polynomial reconstructibility of the matching polynomial. We collect previous results, prove it for graphs with pendant edges and disprove it for some graphs.
Some classes of bipartite graphs induced by Gray codes I Nengah Suparta
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.2017.5.2.12

Abstract

A Gray code of length n is a list of all binary words of length n such that each two successive codewords differ in only one bit position. If the first and the last codewords also share this property, the Gray code is called cyclic, otherwise it is called non-cyclic. The numbers indicating bit positions in where two successive codewords differ in the list of Gray codes are called transition numbers, and the sequence of these all numbers is called the transition sequence of the Gray code. In this article, bit positions of a Gray code of length n will be counted from 1 up until n. If a graph with vertex set {1, 2, ..., n} having the property that two vertices i and j are adjacent in the graph if and only if, i and j are consecutive transitions in the transition sequence of a Gray code, then the graph is called induced by the Gray code. Some classes of bipartite graphs are shown to be induced by Gray codes. Particularly, we show that complete bipartite graphs are induced by Gray codes. 
Independent strong domination in complementary prisms Zeynep Nihan Berberler; Murat Ersen Berberler
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 8, No 1 (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.2020.8.1.1

Abstract

Let G = (V, E) be a graph and u,v ∈ V. Then, u strongly dominates  v if (i) uv ∈ E  and (ii) deg(u) ≥ deg(v). A set D ⊂ V  is a strong-dominating set of  G  if every vertex in V-D is strongly dominated by at least one vertex in D. A set D ⊆ V  is an independent set if no two vertices of D  are adjacent. The independent strong domination number is(G) of a graph G is the minimum cardinality of a strong dominating set which is independent. Let Ġ   be the complement of a graph G. The complementary prism GĠ  of G  is the graph formed from the disjoint union of G  and  Ġ by adding the edges of a perfect matching between the corresponding vertices of G and Ġ. In this paper, we consider the independent strong domination in complementary prisms, characterize the complementary prisms with small independent strong domination numbers, and investigate the relationship between independent strong domination number and the distance-based parameters.
On d-antimagic labelings of plane graphs Martin Baca; Ljiljana Brankovic; Marcela Lascsakova; Oudone Phanalasy; Andrea Semanicova-Fenovciova
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 1, No 1 (2013): 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.2013.1.1.3

Abstract

The paper deals with the problem of labeling the vertices and edges of a plane graph in such a way that the labels of the vertices and edges surrounding that face add up to a weight of that face. A labeling of a plane graph is called d-antimagic if for every positive integer s, the s-sided face weights form an arithmetic progression with a difference d. Such a labeling is called super if the smallest possible labels appear on the vertices. In the paper we examine the existence of such labelings for several families of plane graphs.
On equitable coloring of corona of wheels J. Vernold Vivin; K. Kaliraj
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 4, No 2 (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.2016.4.2.8

Abstract

The notion of equitable colorability was introduced by Meyer in $1973$ \cite{meyer}. In this paper we obtain interesting results regarding the equitable chromatic number $\chi_{=}$ for the corona graph of a simple graph with a wheel graph $G\circ W_n$. Some extensions into $l$-corona products are also determined.
Graceful labeling of triangular extension of complete bipartite graph Sarbari Mitra; Soumya Bhoumik
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 7, No 1 (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.2019.7.1.2

Abstract

For positive integers m, n, Km, n represents the complete bipartite graph. We name the graph G = Km, n ⊙ K2 as triangular extension of complete bipartite graph Km, n, since there is a triangle hanging from every vertex of Km, n. In this paper we show that G is graceful when m = n = 2ℓ, for any integer ℓ.
On energy, Laplacian energy and $p$-fold graphs Hilal A Ganie; Shariefuddin Pirzada; Edy Tri Baskoro
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 3, No 1 (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.2015.3.1.10

Abstract

For a graph $G$ having adjacency spectrum ($A$-spectrum) $\lambda_n\leq\lambda_{n-1}\leq\cdots\leq\lambda_1$ and Laplacian spectrum ($L$-spectrum) $0=\mu_n\leq\mu_{n-1}\leq\cdots\leq\mu_1$, the energy is defined as $ E(G)=\sum_{i=1}^{n}|\lambda_i|$ and the Laplacian energy is defined as $LE(G)=\sum_{i=1}^{n}|\mu_i-\frac{2m}{n}|$. In this paper, we give upper and lower bounds for the energy of $KK_n^j,~1\leq j \leq n$ and as a consequence we generalize a result of Stevanovic et al. [More on the relation between Energy and Laplacian energy of graphs, MATCH Commun. Math. Comput. Chem. {\bf 61} (2009) 395-401]. We also consider strong double graph and strong $p$-fold graph to construct some new families of graphs $G$ for which $E(G)> LE(G)$.

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