Results 31 to 40 of about 2,584 (237)
Total Edge Irregularity Strength of Arithmetic Book Graphs
Journal of Physics: Conference Series, 2019 Abstract For any simple undirected graph G(V, E), a map f : V ⋃ E → {1, 2, …, k} such that for any different edges xy and x’y’ their weights are distinct is called an edge irregular total k-labeling. The weight of edge xy is defined as the sum of edge label of xy, vertex label of x and vertex label of y. The minimum k for which the graph
Lucia Ratnasari +4 more
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Indonesian Journal of Combinatorics, 2020 Given graph G(V,E). We use the notion of total k-labeling which is edge irregular. The notion of total edge irregularity strength (tes) of graph G means the minimum integer k used in the edge irregular total k-labeling of G.
Isnaini Rosyida, Diari Indriati
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Total Edge Irregularity Strength for Graphs
, 2017 An edge irregular total $k$-labelling $f : V(G)\cup E(G)\rightarrow \{1,2,\dots,k\}$ of a graph $G$ is a labelling of the vertices and the edges of $G$ in such a way that any two different edges have distinct weights. The weight of an edge $e$, denoted by $wt(e)$, is defined as the sum of the label of $e$ and the labels of two vertices which incident ...
Irwansyah, M, Salman A. N.
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Generalized Arithmetic Staircase Graphs and Their Total Edge Irregularity Strengths
Symmetry, 2022 Let Γ=(VΓ,EΓ) be a simple undirected graph with finite vertex set VΓ and edge set EΓ. A total n-labeling α:VΓ∪EΓ→{1,2,…,n} is called a total edge irregular labeling on Γ if for any two different edges xy and x′y′ in EΓ the numbers α(x)+α(xy)+α(y) and α(x′)+α(x′y′)+α(y′) are distinct. The smallest positive integer n such that Γ can be labeled by a total
Yeni Susanti +4 more
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On Edge Irregular Reflexive Labeling for Generalized Prism
Journal of Mathematics, 2022 Among the various ideas that appear while studying graph theory, which has gained much attraction especially in graph labeling, labeling of graphs gives mathematical models which value for a vast range of applications in high technology (data security ...
Chenxi Wang +5 more
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Irregular labelings of helm and sun graphs
AKCE International Journal of Graphs and Combinatorics, 2015 A vertex irregular total k-labeling of a (p,q)-graph G=(V,E) is a labeling ϕ:V∪E→{1,2,…,k} such that the weights of the vertices wt(v)=ϕ(v)+∑uv∈Eϕ(uv) are different for all vertices.
Ali Ahmad +2 more
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Total edge irregularity strength of large graphs
Discrete Mathematics, 2012 Let $m:=|E(G)|$ sufficiently large and $s:=(m-1)/3$. We show that unless the maximum degree $ > 2s$, there is a weighting $w:E\cup V\to \{0,1,...,s\}$ so that $w(uv)+w(u)+w(v)\ne w(u'v')+w(u')+w(v')$ whenever $uv\ne u'v'$ (such a weighting is called {\em total edge irregular}).
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On cycle-irregularity strength of ladders and fan graphs
Electronic Journal of Graph Theory and Applications, 2020 A simple graph G = (V(G),E(G)) admits an H-covering if every edge in E(G) belongs to at least one subgraph of G isomorphic to a given graph H. A total k-labeling φ : V(G) ∪ E(G) → {1,2,..., k} is called to be an H-irregular total k-labeling of the graph ...
Faraha Ashraf +3 more
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The total disjoint irregularity strength of some certain graphs
Indonesian Journal of Combinatorics, 2020 Under a totally irregular total k-labeling of a graph G = (V, E), we found that for some certain graphs, the edge-weight set W (E) and the vertex-weight set W (V ) of G which are induced by k=ts(G), W(E)∩W(V) is a non empty set.
Meilin I Tilukay, A. N. M. Salman
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Totally irregular total labeling of some caterpillar graphs
Electronic Journal of Graph Theory and Applications, 2020 Assume that G(V,E) is a graph with V and E as its vertex and edge sets, respectively. We have G is simple, connected, and undirected. Given a function λ from a union of V and E into a set of k-integers from 1 until k.
Diari Indriati +4 more
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