Results 11 to 20 of about 15,436 (257)
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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Upper bounds on distance vertex irregularity strength of some families of graphs [PDF]
Opuscula Mathematica, 2022 For a graph \(G\) its distance vertex irregularity strength is the smallest integer \(k\) for which one can find a labeling \(f: V(G)\to \{1, 2, \dots, k\}\) such that \[ \sum_{x\in N(v)}f(x)\neq \sum_{x\in N(u)}f(x)\] for all vertices \(u,v\) of \(G\),
Sylwia Cichacz +2 more
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Distance irregularity strength of graphs with pendant vertices [PDF]
Opuscula Mathematica, 2022 A vertex \(k\)-labeling \(\phi:V(G)\rightarrow\{1,2,\dots,k\}\) on a simple graph \(G\) is said to be a distance irregular vertex \(k\)-labeling of \(G\) if the weights of all vertices of \(G\) are pairwise distinct, where the weight of a vertex is the ...
Faisal Susanto +3 more
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Two types irregular labelling on dodecahedral modified generalization graph
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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On graph irregularity strength [PDF]
Journal of Graph Theory, 2002 AbstractAn assignment of positive integer weights to the edges of a simple graph G is called irregular, if the weighted degrees of the vertices are all different. The irregularity strength, s(G), is the maximal weight, minimized over all irregular assignments.
Frieze, Alan +3 more
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Total edge irregularity strength of some cycle related graphs
Indonesian Journal of Combinatorics, 2021 An edge irregular total k-labeling f : V ∪ E → 1,2, ..., k of a graph G = (V,E) is a labeling of vertices and edges of G in such a way that for any two different edges uv and u'v', their weights f(u)+f(uv)+f(v) and f(u')+f(u'v')+f(v') are distinct.
Ramalakshmi Rajendran, Kathiresan KM
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Total edge irregularity strength of quadruplet and quintuplet book graphs [PDF]
ITM Web of Conferences, 2021 Let G= (V, E) be a finite, simple and undirected graph with a vertex set V and an edge set E. An edge irregular total k-labelling is a function f : V ᴗE → {1,2,…,k} such that for any two different edges xy and x’y’ in E, their weights are distinct.
Ratnasari Lucia +3 more
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Group irregularity strength of connected graphs [PDF]
Journal of Combinatorial Optimization, 2013 We investigate the group irregularity strength ($s_g(G)$) of graphs, i.e. the smallest value of $s$ such that taking any Abelian group $\gr$ of order $s$, there exists a function $f:E(G)\rightarrow \gr$ such that the sums of edge labels at every vertex are distinct.
Anholcer, Marcin +2 more
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Total vertex irregularity strength for trees with many vertices of degree two
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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On the edge irregularity strength of corona product of cycle with isolated vertices
AKCE International Journal of Graphs and Combinatorics, 2016 In this paper, we investigate the new graph characteristic, the edge irregularity strength, denoted as es, as a modification of the well known irregularity strength, total edge irregularity strength and total vertex irregularity strength. As a result, we
I. Tarawneh, R. Hasni, A. Ahmad
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