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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 15 Documents
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Search results for , issue "Vol 7, No 2 (2019): Electronic Journal of Graph Theory and Applications" : 15 Documents clear
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.
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.
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.
On the Steiner antipodal number of graphs S. Arockiaraj; R. Gurusamy; KM. Kathiresan
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.2019.7.2.3

Abstract

The Steiner n-antipodal graph of a graph G on p vertices, denoted by SAn(G),  has the same vertex set as G and any n(2 ≤ n ≤ p) vertices are mutually adjacent in SAn(G) if and only if they are n-antipodal in G. When G is disconnected, any n vertices are mutually adjacent in SAn(G) if not all of them are in the same component. SAn(G) coincides with the antipodal graph A(G) when n = 2. The least positive integer n such that SAn(G) ≅ H, for a pair of graphs G and H on p vertices, is called the Steiner A-completion number of G over H. When H = Kp,  the Steiner A-completion number of G over H is called the Steiner antipodal number of G. In this article, we obtain the Steiner antipodal number of some families of graphs and for any tree. For every positive integer k,  there exists a tree having Steiner antipodal number k and there exists a unicyclic graph having Steiner antipodal number k. Also we show that the notion of the Steiner antipodal number of graphs is independent of the Steiner radial number, the domination number and the chromatic number of graphs.
Bounds for graph energy in terms of vertex covering and clique numbers Hilal A. Ganie; U. Samee; S. Pirzada; Ahmad M. Alghamadi
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.2019.7.2.9

Abstract

Let G be a simple graph with n vertices, m edges and having adjacency eigenvalues λ1, λ2, …, λn. The energy E(G) of the graph G is defined as E(G) = ∑i = 1n∣λi∣. In this paper, we obtain the upper bounds for the energy E(G) in terms of the vertex covering number τ, the clique number ω, the number of edges m, maximum vertex degree d1 and second maximum vertex degree d2 of the connected graph G. These upper bounds improve some of the recently known upper bounds.
Cycle decompositions and constructive characterizations Irene Heinrich; Manuel Streicher
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.2019.7.2.15

Abstract

Decomposing an Eulerian graph into a minimum respectively maximum number of edge disjoint cycles is an NP-complete problem. We prove that an Eulerian graph decomposes into a unique number of cycles if and only if it does not contain two edge disjoint cycles sharing three or more vertices. To this end, we discuss the interplay of three binary graph operators leading to novel constructive characterizations of two subclasses of Eulerian graphs. This enables us to present a polynomial-time algorithm which decides whether the number of cycles in a cycle decomposition of a given Eulerian graph is unique.
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.
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.
A method to construct graphs with certain partition dimension Debi Oktia Haryeni; Edy Tri Baskoro; Suhadi Wido Saputro
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.2019.7.2.5

Abstract

In this paper, we propose a method for constructing new graphs from a given graph G so that the resulting graphs have the partition dimension at most one larger than the partition dimension of the graph G. In particular, we employ this method to construct a family of graphs with partition dimension 3.
Counting and labeling grid related graphs Christian Barrientos; Sarah Minion
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.2019.7.2.11

Abstract

In this work we explore some graphs associated with the grid Pm × Pn. A fence is any subgraph of the grid obtained by deleting any feasible number of edges from some or all the copies of Pm. We present here a closed formula for the number of non-isomorphic fences obtained from Pm × Pn, for every m, n ≥ 2. A rigid grid is a supergraph of the grid, where for every square a pair of opposite vertices are connected; we show that the number of fences built on Pm × Pn is the same that the number of rigid grids built on Pm × Pn + 1. We also introduce a substitution scheme that allows us to substitute any interior edge of any Pm in an α-labeled copy of Pm × Pn to obtain a new graph with an α-labeling. This process can be iterated multiple times on the n copies of Pm; in this way we prove the existence of an α-labeling for any graph obtained via these substitutions; these graphs form a quite robust family of α-graphs where the grid is one of its members. We also show two subfamilies of disconnected graphs that can be obtained using this scheme, proving in that way that they are also α-graphs.

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