Results 1 to 10 of about 597 (229)
On Total Vertex Irregularity Strength of Hexagonal Cluster Graphs [PDF]
International Journal of Mathematics and Mathematical Sciences, 2021 For a simple graph G with a vertex set VG and an edge set EG, a labeling f:VG∪EG⟶1,2,⋯,k is called a vertex irregular total k−labeling of G if for any two different vertices x and y in VG we have wtx≠wty where wtx=fx+∑u∈VGfxu.
Nurdin Hinding +3 more
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Counterexamples to the total vertex irregularity strength’s conjectures [PDF]
Discrete Mathematics Letters, 2023 Summary: The total vertex irregularity strength \(\mathrm{tvs}(G)\) of a simple graph \(G(V, E)\) is the smallest positive integer \(k\) so that there exists a function \(\varphi:V \cup E \rightarrow [1, k]\) provided that all vertex-weights are distinct, where a vertex-weight is the sum of labels of a vertex and all of its incident edges. In the paper
Faisal Susanto +2 more
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Two types irregular labelling on dodecahedral modified generalization graph [PDF]
Heliyon, 2022 Irregular labelling on graph is a function from component of graph to non-negative natural number such that the weight of all vertices, or edges are distinct. The component of graph is a set of vertices, a set of edges, or a set of both. In this paper we
Nurdin Hinding +4 more
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Total vertex irregularity strength of trees with maximum degree five [PDF]
Electronic Journal of Graph Theory and Applications, 2018 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
S. Susilawati +2 more
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Total vertex irregularity strength for trees with many vertices of degree two [PDF]
Electronic Journal of Graph Theory and Applications, 2020 For a simple graph G = (V,E), a mapping φ : V ∪ E → {1,2,...,k} is defined as a vertex irregular total k-labeling of G if for every two different vertices x and y, wt(x) ≠ wt(y), where wt(x) = φ(x)+ Σxy∈E(G) φ(xy).
Rinovia Simanjuntak +2 more
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Computation of Total Vertex Irregularity Strength of Theta Graphs [PDF]
IEEE Access, 2019 A total labeling $\phi: V(G)\cup E(G) \to \{1,2, {\dots }, k\}$ is called a vertex irregular total $k$ -labeling of a graph $G$ if different vertices in $G$ have different weights.
Ali N. A. Koam, Ali Ahmad
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TOTAL EDGE AND VERTEX IRREGULAR STRENGTH OF TWITTER NETWORK
Barekeng, 2022 Twitter data can be converted into a graph where users can represent the vertices. Then the edges can be represented as relationships between users. This research focused on determining the total edge irregularity strength (tes) and the total vertices ...
Edy Saputra Rusdi, Nur Hilal A. Syahrir
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Total vertex product irregularity strength of graphs
Discussiones Mathematicae Graph TheoryConsider a simple graph $G$. We call a labeling $w:E(G)\cup V(G)\rightarrow \{1, 2, \dots, s\}$ (\textit{total vertex}) \textit{product-irregular}, if all product degrees $pd_G(v)$ induced by this labeling are distinct, where $pd_G(v)=w(v)\times\prod_{e\ni v}w(e)$.
Marcin Anholcer +2 more
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Total vertex irregularity strength of comb product of two cycles [PDF]
MATEC Web of Conferences, 2018 Let G = (V (G),E(G)) be a graph and k be a positive integer. A total k-labeling of G is a map f : V (G) ∪ E(G) → {1,2...,k}. The vertex weight v under the labeling f is denoted by Wf(v) and defined by Wf(v) = f(v) + Σuv∈E(G)f(uv). A total k-labeling of G
Ramdani Rismawati, Ramdhani Muhammad Ali
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Optimizing hybrid network topologies in communication networks through irregularity strength [PDF]
Scientific ReportsGraph theory has emerged as an influential tool for communication network design and analysis, especially for designing hybrid network topologies for local area networks (LANs).
Syed Aqib Abbas Naqvi +5 more
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