Neighbor sum distinguishing list total coloring of subcubic graphs

You Lu (), Chuandong Xu () and Zhengke Miao ()
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You Lu: Northwestern Polytechnical University
Chuandong Xu: Xidian University
Zhengke Miao: Jiangsu Normal University

Journal of Combinatorial Optimization, 2018, vol. 35, issue 3, No 7, 778-793

Abstract: Abstract Let $$G=(V, E)$$ G = ( V , E ) be a simple graph and denote the set of edges incident to a vertex v by E(v). The neighbor sum distinguishing (NSD) total choice number of G, denoted by $$\mathrm{ch}_{\Sigma }^{t}(G)$$ ch Σ t ( G ) , is the smallest integer k such that, after assigning each $$z\in V\cup E$$ z ∈ V ∪ E a set L(z) of k real numbers, G has a total coloring $$\phi $$ ϕ satisfying $$\phi (z)\in L(z)$$ ϕ ( z ) ∈ L ( z ) for each $$z\in V\cup E$$ z ∈ V ∪ E and $$\sum _{z\in E(u)\cup \{u\}}\phi (z)\ne \sum _{z\in E(v)\cup \{v\}}\phi (z)$$ ∑ z ∈ E ( u ) ∪ { u } ϕ ( z ) ≠ ∑ z ∈ E ( v ) ∪ { v } ϕ ( z ) for each $$uv\in E$$ u v ∈ E . In this paper, we propose some reducible configurations of NSD list total coloring for general graphs by applying the Combinatorial Nullstellensatz. As an application, we present that $$\mathrm{ch}^{t}_{\Sigma }(G)\le \Delta (G)+3$$ ch Σ t ( G ) ≤ Δ ( G ) + 3 for every subcubic graph G.

Keywords: List total coloring; Neighbor sum distinguishing; Reducible configuration (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s10878-017-0239-5

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