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Research PaperNo Access

On generalized neighbor sum distinguishing index of planar graphs

    https://doi.org/10.1142/S1793830921501470Cited by:0 (Source: Crossref)
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    Abstract

    For a proper k-edge coloring ϕ:E(G)→{1,2,…,k} of a graph G, let w(v) denote the sum of the colors taken on the edges incident to the vertex v. Given a positive integer p, the Σp-neighbor sum distinguishing k-edge coloring of G is ϕ such that for each edge uv∈E(G), |w(v)−w(u)|≥p. We denote the smallest integer k in such coloring of G by χΣp′(G). For p=1, Wang et al. proved that χΣ1′(G)≤max{Δ(G)+10,25}. In this paper, we show that if G is a planar graph without isolated edges, then χΣp′(G)≤max{Δ(G)+(16p−6),f(p)}, where f(p)=max{22p+3,8p2+26p+1+(2p+1)16p2+96p−154}.

    Communicated by Weili Wu

    AMSC: 05C15

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