Remarks on Fractional Locally Harmonious Coloring

Gao, Wei

doi:10.30538/oms2018.0036

Cited by 3 publications

(1 citation statement)

References 9 publications

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“…As a matter of fact, disjoint union of a graph is the relationship between its isomorphic copies keeping the structural properties intact and used to create new larger structures having the same properties as the base graph have. In future, one can extend this idea to find the results for larger differences and for more general structure with applications in theoretical computer science [14][15][16].…”

Section: Resultsmentioning

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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Section: Resultsmentioning

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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Radio Number for Generalized Petersen Graphs $P(n,2)$

et al. 2019

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Let G be a connected graph and d(µ, ω) be the distance between any two vertices of G. The diameter of G is denoted by diam(G) and is equal to max{d(µ, ω); µ, ω ∈ G}. The radio labeling (RL) for the graph G is an injective function : V (G) → N ∪ {0} such that for any pair of vertices µ andThe span of radio labeling is the largest number in (V ). The radio number of G, denoted by rn(G) is the minimum span over all radio labeling of G. In this paper, we determine radio number for the generalized Petersen graphs, P(n, 2), n = 4k +2. Further the lower bound of radio number for P(n, 2) when n = 4k is determined.INDEX TERMS Diameter, radio number, generalized Petersen graph.

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Antimagicness of $mC_n$ -Path and Its Disjoint Union

Umar²,

Habib

et al. 2019

IEEE Access

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Let M = (V (M), E(M)) be a simple graph with finite vertices and edges. An N-covering of M is a family {N 1 , N 2 ,. .. , N α } of subgraphs of M isomorphic to N such that every edge in E(M) belongs to N l , for some l, l ∈ {1, 2,. .. , α}. Such a graph is a (c, d)-N-antimagic if ∃ a bijection ψ : V M ∪E M → {1, 2,. .. , |V M |+|E M |} such that for all N l ∼ = N , {wt ψ (N l)} = {c, c+d,. .. , c+(α −1)d}. For ψ(V (M)) = {1, 2, 3,. .. , |V (M)|}, the labeling ψ would be super (c, d)-N-antimagic and for d = 0 it would be N-supermagic. In this manuscript, we investigated that mC n-path has super (c, d)-C n-antimagic labeling for differences d ∈ {0, 1,. .. , 5} and extend the result for C n-supermagic labeling of disjoint union of isomorphic copies of mC n-path. INDEX TERMS Block cut-vertex graph, mC n-path, disjoint union of mC n-path, super (c, d)-C n-antimagic.

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Remarks on Fractional Locally Harmonious Coloring

Abstract: Locally harmonious coloring is a relax version of standard harmonious coloring which only needs that the color pairs for adjacent edges are different. In this remark, we introduce the concept of fractional locally harmonious coloring, and present some basic facts for this coloring.

Cited by 3 publications

References 9 publications

Tree-Antimagicness of Web Graphs and Their Disjoint Union

Tree-Antimagicness of Web Graphs and Their Disjoint Union

Radio Number for Generalized Petersen Graphs $P(n,2)$

Antimagicness of $mC_n$ -Path and Its Disjoint Union

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