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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 325 Documents
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Spanning k-ended trees of 3-regular connected graphs Hamed Ghasemian Zoeram; Daniel Yaqubi
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.2017.5.2.4

Abstract

A vertex of degree one is called an end-vertex and the set of end-vertices of G is denoted by End(G). For a positive integer k, a tree T be called k-ended tree if $|End(T)| \leq k$. In this paper, we obtain sufficient conditions for spanning k-trees of 3-regular connected graphs. We give a construction sequence of graphs satisfying the condition. At the end, we present a conjecture about spanning k-ended trees of 3-regular connected graphs.
Squared distance matrix of a weighted tree Ravindra B. Bapat
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.2019.7.2.8

Abstract

Let T be a tree with vertex set {1, …, n} such that each edge is assigned a nonzero weight. The squared distance matrix of T,  denoted by Δ,  is the n × n matrix with (i, j)-element d(i, j)2,  where d(i, j) is the sum of the weights of the edges on the (ij)-path. We obtain a formula for the determinant of Δ. A formula for Δ − 1 is also obtained, under certain conditions. The results generalize known formulas for the unweighted case.
Bounds on weak and strong total domination in graphs M.H. Akhbari; Nader Jafari Rad
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.2016.4.1.10

Abstract

A set $D$ of vertices in a graph $G=(V,E)$ is a total dominatingset if every vertex of $G$ is adjacent to some vertex in $D$. Atotal dominating set $D$ of $G$ is said to be weak if everyvertex $v\in V-D$ is adjacent to a vertex $u\in D$ such that$d_{G}(v)\geq d_{G}(u)$. The weak total domination number$\gamma_{wt}(G)$ of $G$ is the minimum cardinality of a weaktotal dominating set of $G$. A total dominating set $D$ of $G$ issaid to be strong if every vertex $v\in V-D$ is adjacent to avertex $u\in D$ such that $d_{G}(v)\leq d_{G}(u)$. The strongtotal domination number $\gamma_{st}(G)$ of $G$ is the minimumcardinality of a strong total dominating set of $G$. We presentsome bounds on weak and strong total domination number of a graph.
Parsimonious edge-coloring on surfaces Sarah-Marie Belcastro
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.2018.6.2.9

Abstract

We correct a small error in a 1996 paper of Albertson and Haas, and extend their lower bound for the fraction of properly colorable edges of planar subcubic graphs that are simple, connected, bridgeless, and edge-maximal to other surface embeddings of subcubic graphs.
The geodetic domination number of comb product graphs Dimas Agus Fahrudin; Suhadi Wido Saputro
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.2020.8.2.13

Abstract

A subset S of vertices in graph G is called a geodetic set if every vertex in V(G) \ S lies on a shortest path between two vertices in S. A subset S of vertices in G is called a dominating set if every vertex in V(G) \  S is adjacent to a vertex in S. The set S is called a geodetic dominating set if S is both geodetic and dominating sets. The geodetic domination number of G, denoted by γg(G), is the minimum cardinality of geodetic domination sets in G. The comb product of connected graphs G and H at vertex o ∈ V(H), denoted by  G ∇o H, is a graph obtained by taking one copy of G and |V(G)| copies of H and identifying the ith copy of H at the vertex o to the ith vertex of G. In this paper, we determine an exact value of γg(G ∇o H) for any connected graphs G and H.
On scores, losing scores and total scores in hypertournaments Shariefuddin Pirzada; Muhammad Ali Khan; Zhou Guofei; Koko K Kayibi
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.2015.3.1.2

Abstract

A $k$-hypertournament is a complete $k$-hypergraph with each $k$-edge endowed with an orientation, that is, a linear arrangement of the vertices contained in the edge. In a $k$-hypertournament, the score $s_{i}$ (losing score $r_{i}$) of a vertex $v_{i}$ is the number of arcs containing $v_{i}$ in which $v_{i}$ is not the last element (in which $v_{i}$ is the last element). The total score of $v_{i}$ is defined as $t_{i}=s_{i}-r_{i}$. In this paper we obtain stronger inequalities for the quantities $\sum_{i\in I}r_{i}$, $\sum_{i\in I}s_{i}$ and $\sum_{i\in I}t_{i}$, where $I\subseteq \{ 1,2,\ldots,n\}$. Furthermore, we discuss the case of equality for these inequalities. We also characterize total score sequences of strong $k$-hypertournaments.
Bounds for the Laplacian spectral radius of graphs Kamal Lochan Patra; Binod Kumar Sahoo
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.2017.5.2.10

Abstract

This paper is a survey on the upper and lower bounds for the largest eigenvalue of the Laplacian matrix, known as the Laplacian spectral radius, of a graph. The bounds are given as functions of graph parameters like the number of vertices, the number of edges, degree sequence, average 2-degrees, diameter, covering number, domination number, independence number and other parameters.
Designs for graphs with six vertices and ten edges A. D. Forbes; T. S. Griggs; K. A. Forbes
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.2019.7.2.14

Abstract

The design spectrum has been determined for two of the 15 graphs with six vertices and ten edges. In this paper we completely solve the design spectrum problem for a further eight of these graphs.
Forbidden subgraph pairs for traceability of block-chains Binlong Li; Hajo Broersma; Shenggui Zhang
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.2013.1.1.1

Abstract

A block-chain is a graph whose block graph is a path, i.e. it is either a $P_1$, a $P_2$, or a 2-connected graph, or a graph of connectivity 1 with exactly two end-blocks. A graph is called traceable if it contains a Hamilton path. A traceable graph is clearly a block-chain, but the reverse does not hold in general.In this paper we characterize all pairs of connected graphs $\{R,S\}$ such that every $\{R,S\}$-free block-chain is traceable.
About the second neighborhood problem in tournaments missing disjoint stars Salman Ghazal
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.2016.4.2.6

Abstract

Let $D$ be a digraph without digons. Seymour's second neighborhood conjecture states that $D$ has a vertex $v$ such that $d^+(v) \leq d^{++}(v)$. Under some conditions, we prove this conjecture for digraphs missing $n$ disjoint stars. Weaker conditions are required when $n = 2$ or $3$. In some cases we exhibit two such vertices.

Page 2 of 33 | Total Record : 325

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