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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 d-Fibonacci digraphs C. Dalfó; M.A. Fiol
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 9, No 2 (2021): 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.2021.9.2.22

Abstract

The d-Fibonacci digraphs F(d, k), introduced here, have the number of vertices following some generalized Fibonacci-like sequences. They can be defined both as digraphs on alphabets and as iterated line digraphs. Here we study some of their nice properties. For instance, F(d, k) has diameter d + k − 2 and is semi-pancyclic; that is, it has a cycle of every length between 1 and ℓ, with ℓ ∈ {2k − 2, 2k − 1}. Moreover, it turns out that several other numbers of F(d, k) (of closed l-walks, classes of vertices, etc.) also follow the same linear recurrences as the numbers of vertices of the d-Fibonacci digraphs.
The integer-antimagic spectra of Hamiltonian graphs Ugur Odabasi; Dan Roberts; Richard M. Low
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 9, No 2 (2021): 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.2021.9.2.5

Abstract

Let A be a nontrivial abelian group. A connected simple graph G = (V, E) is A-antimagic, if there exists an edge labeling f : E(G)→A ∖ {0A} such that the induced vertex labeling f+(v)=∑{u, v}∈E(G)f({u, v}) is a one-to-one map. The integer-antimagic spectrum of a graph G is the set IAM (G)={k : G is ℤk-antimagic and k ≥ 2}. In this paper, we determine the integer-antimagic spectra for all Hamiltonian graphs.
Complete bipartite graph is a totally irregular total graph Meilin I. Tilukay; Pranaya D. M. Taihuttu; A. N. M. Salman; Francis Y. Rumlawang; Zeth A. Leleury
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 9, No 2 (2021): 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.2021.9.2.11

Abstract

A graph G is called a totally irregular total k-graph if it has a totally irregular total k-labeling λ : V ∪ E→ 1, 2, ... , k, that is a total labeling such that for any pair of different vertices x and y of G, their weights wt(x) and wt(y) are distinct, and for any pair of different edges e and f of G, their weights wt(e) and wt(f) are distinct. The minimum value k under labeling λ is called the total irregularity strength of G, denoted by ts(G). For special cases of a complete bipartite graph Km, n, the ts(K1, n) and the ts(Kn, n) are already determined for any positive integer n. Completing the results, this paper deals with the total irregularity strength of complete bipartite graph Km, n for any positive integer m and n.
On maximum packings of λ-fold complete 3-uniform hypergraphs with triple-hyperstars of size 4 Amber Armstrong; Ryan C. Bunge; William Duncan; Saad I. El-Zanati; Kristin Koe; Rachel Stutzman
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 9, No 2 (2021): 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.2021.9.2.17

Abstract

A symmetric triple-hyperstar is a connected, 3-uniform hypergraph where, for some edge {a, b, c}, vertices a, b, and c all have degree k > 1 and all other edges contain exactly 2 vertices of degree 1. Let H denote the symmetric triple-hyperstar with 4 edges and, for positive integers λ and v, let λKv(3) denote the λ-fold complete 3-uniform hypergraph on v vertices. We find maximum packings of λKv(3) with copies of H.
Determining finite connected graphs along the quadratic embedding constants of paths Edy Tri Baskoro; Nobuaki Obata
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 9, No 2 (2021): 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.2021.9.2.23

Abstract

The QE constant of a finite connected graph G, denoted by QEC(G), is by definition the maximum of the quadratic function associated to the distance matrix on a certain sphere of codimension two. We prove that the QE constants of paths Pn form a strictly increasing sequence converging to −1/2. Then we formulate the problem of determining all the graphs G satisfying QEC(Pn)≤QEC(G)<QEC(Pn + 1). The answer is given for n = 2 and n = 3 by exploiting forbidden subgraphs for QEC(G)< − 1/2 and the explicit QE constants of star products of the complete graphs.
Integrity of total transformation graphs B Basavanagoud; Praveen Jakkannavar; Shruti Policepatil
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 9, No 2 (2021): 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.2021.9.2.6

Abstract

A communication network can be considered to be highly vulnerable to disruption if the failure of few members (nodes or links) can result in no member’s being able to communicate with very many others. These communication networks can be modeled through graphs, and we have several graph-theoretic parameters (viz., connectivity, edge-connectivity, tenacity etc.,) to describe the stability of graphs. But, these parameters are not sufficient to study stability of graphs. This leads to the concept of integrity of a graph. The integrity of a graph will consider both the damage and the maximum possible capacity of communication corresponding to the maximum damage to the network. Therefore, we discuss the integrity of total transformation graphs which can help us to reconstruct the given network in such a way that it is more stable than the earlier one. If the network is modeled through total transformation graphs, then there will be increase in the number of nodes and links between the nodes in the obtained network which automatically cause the increase in the stability of the network. In this paper, we obtain the integrity of total transformation graphs of some special class of graphs. Further, we present bounds of integrity of some total transformation graphs of a graph in terms of number of vertices, number of edges and integrity of some derived graph appears as induced subgraph. The expression for integrity of total graph of cycle which was given by Qingfang Ye contained an error. We give correct version of it. In addition, we compute integrity of book graphs.
Anti-Ramsey Hypergraph Numbers Mark Budden; William Stiles
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 9, No 2 (2021): 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.2021.9.2.12

Abstract

The anti-Ramsey number arn(H) of an r-uniform hypergraph is the maximum number of colors that can be used to color the hyperedges of a complete r-uniform hypergraph on n vertices without producing a rainbow copy of H. In this paper, we determine anti-Ramsey numbers for paths of length 2, certain stars and complete hypergraphs, and the complete 3-uniform hypergraph of order 4 with a single hyperedge removed.
Unique response strong Roman dominating functions of graphs Doost Ali Mojdeh; Guoliang Hao; Iman Masoumi; Ali Parsian
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 9, No 2 (2021): 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.2021.9.2.18

Abstract

Given a simple graph G=(V,E) with maximum degree Δ. Let (V0, V1, V2) be an ordered partition of V, where Vi = {v ∈ V : f(v)=i} for i = 0, 1 and V2 = {v ∈ V : f(v)≥2}. A function f : V → {0, 1, …, ⌈Δ/2⌉+1} is a strong Roman dominating function (StRDF) on G, if every v ∈ V0 has a neighbor w ∈ V2 and f(w)≥1 + ⌈1/2|N(w)∩V0|⌉. A function f : V → {0, 1, …, ⌈Δ/2⌉+1} is a unique response strong Roman function (URStRF), if w ∈ V0, then |N(w)∩V2|≤1 and w ∈ V1 ∪ V2 implies that |N(w)∩V2|=0. A function f : V → {0, 1, …, ⌈Δ/2⌉+1} is a unique response strong Roman dominating function (URStRDF) if it is both URStRF and StRDF. The unique response strong Roman domination number of G, denoted by uStR(G), is the minimum weight of a unique response strong Roman dominating function. In this paper we approach the problem of a Roman domination-type defensive strategy under multiple simultaneous attacks and begin with the study of several mathematical properties of this invariant. We obtain several bounds on such a parameter and give some realizability results for it. Moreover, for any tree T of order n ≥ 3 we prove the sharp bound uStR(T)≤8n/9.
A note on the Ramsey number for cycle with respect to multiple copies of wheels I Wayan Sudarsana
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 9, No 2 (2021): 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.2021.9.2.24

Abstract

Let Kn be a complete graph with n vertices. For graphs G and H, the Ramsey number R(G, H) is the smallest positive integer n such that in every red-blue coloring on the edges of Kn, there is a red copy of graph G or a blue copy of graph H in Kn. Determining the Ramsey number R(Cn, tWm) for any integers t ≥ 1, n ≥ 3 and m ≥ 4 in general is a challenging problem, but we conjecture that for any integers t ≥ 1 and m ≥ 4, there exists n0 = f(t, m) such that cycle Cn is tWm–good for any n ≥ n0. In this paper, we provide some evidence for the conjecture in the case of m = 4 that if n ≥ n0 then the Ramsey number R(Cn, tW4)=2n + t − 2 with n0 = 15t2 − 4t + 2 and t ≥ 1. Furthermore, if G is a disjoint union of cycles then the Ramsey number R(G, tW4) is also derived.
Non-isomorphic signatures on some generalised Petersen graph Deepak Sehrawat; Bikash Bhattacharjya
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 9, No 2 (2021): 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.2021.9.2.1

Abstract

In this paper we find the number of different signatures of P(3, 1),P(5, 1) and P(7, 1) up to switching isomorphism, where P(n, k) denotes the generalised Petersen graph, 2k < n. We also count the number of non-isomorphic signatures on P(2n + 1, 1) of size two for all n ≥ 1, and we conjecture that any signature of P(2n + 1, 1), up to switching, is of size at most n + 1.

Page 23 of 39 | Total Record : 382

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