Tree-Antimagicness of Disconnected Graphs

A simple graph G = (V, E) admitting an H-covering is said to be (a, d)-H-antimagic if there exists a bijection f : V ∪ E → {1, 2,. .. , |V | + |E|} such that, for all subgraphs H of G isomorphic to H, wt f (H) = v∈V (H) f (v) + e∈E(H) f (e), form an arithmetic progression a, a + d,. .. , a + (t − 1)d, where a is the first term, d is the common difference and t is the number of subgraphs in the H-covering. Then f is called an (a, d)-H-antimagic labeling. If f (V) = {1, 2,. .. , |V |}, then f is called super (a, d)-H-antimagic labeling. In this paper we investigate the existence of super (a,d)-star-antimagic labelings of a particular class of banana trees and construct a starantimagic graph.

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“…If p = n − 1 then the graph St n−1 n contains n + 1 subgraphs isomorphic to S n . We denote them {S 1 n , S 2 n , . .…”

Section: Super Star-antimagic Graphsmentioning

confidence: 99%

Super (a; d)-star-antimagic graphs

Selvagopal¹,

Jeyanthi²,

Muthuraja³

et al. 2018

HJMS

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“…The existence of super (a, d)-H-antimagic labelings for disconnected graphs is studied in [7]. In [4] it is shown that the disjoint union of multiple copies of a (super) (a, 1)-treeantimagic graph is also a (super) (b, 1)-tree-antimagic. This leads to a natural question.…”

Section: Introductionmentioning

confidence: 99%

Ladders and fan graphs are cycle-antimagic

Bača

Jeyanthi²,

Muthuraja

et al. 2020

Hacettepe Journal of Mathematics and Statistics

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A simple graph G = (V, E) admits an H-covering if every edge in E belongs to at least one subgraph of G isomorphic to a given graph H. The graph G admitting an H-covering is (a, d)-H-antimagic if there exists a bijection f : V ∪ E → {1, 2,. .. , |V | + |E|} such that, for all subgraphs H ′ of G isomorphic to H, the H ′-weights, wt f (H ′) = ∑ v∈V (H ′) f (v) + ∑ e∈E(H ′) f (e), form an arithmetic progression with the initial term a and the common difference d. Such a labeling is called super if the smallest possible labels appear on the vertices. In this paper we prove the existence of super (a, d)-H-antimagic labelings of fan graphs and ladders for H isomorphic to a cycle.

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“…In [1], Gutiérrez and Lladó defined Q-supermagic labelings and the results: P n and C n which are P h -supermagic for some h were proved. Lladó and Moragas [2] investigated C h -magicness of wheels W n , windmills W(n, r), books B n , and of prisms D n for some h. In [3], Baca et al proved results for tree-antimagicness of disconnected graphs. Noshad Ali et al in [4] discussed the C 3 -antimagicness of corona graphs.…”

Section: Introductionmentioning

confidence: 99%

Tree-Antimagicness of Web Graphs and Their Disjoint Union

Zhang

Umar²,

Ren

et al. 2020

Mathematical Problems in Engineering

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In graph theory, the graph labeling is the assignment of labels (represented by integers) to edges and/or vertices of a graph. For a graph G=V,E, with vertex set V and edge set E, a function from V to a set of labels is called a vertex labeling of a graph, and the graph with such a function defined is called a vertex-labeled graph. Similarly, an edge labeling is a function of E to a set of labels, and in this case, the graph is called an edge-labeled graph. In this research article, we focused on studying super ad,d-T4,2-antimagic labeling of web graphs W2,n and isomorphic copies of their disjoint union.

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Tree-Antimagicness of Disconnected Graphs

Cited by 8 publications

References 6 publications

Super (a; d)-star-antimagic graphs

Super (a; d)-star-antimagic graphs

Ladders and fan graphs are cycle-antimagic

Tree-Antimagicness of Web Graphs and Their Disjoint Union

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