Popolno barvanje, ki razlikuje točke v koronskih produktih grafov

An adjacent vertex distinguishing total k-coloring f of a graph G is a proper total k-coloring of G such that no pair of adjacent vertices has the same color sets, where the color set at a vertex v, C_f^G(v), is {f(v)} ∪ {f(vu)|u ∈ V(G), vu ∈ E(G)}. In 2005 Zhang et al. posted the conjecture (AVDTCC) that every simple graph G has adjacent vertex distinguishing total (Δ(G) + 3)-coloring. In this paper we confirm the conjecture for many types of coronas, in particular for generalized, simple and l-coronas of graphs, not relating the results to particular graph classes of the factors.

Publication Details

Journal
Repository of the University of Primorsk (University of Primorska)
Published
2025-03-21
Primary Topic
Graph Labeling and Dimension Problems
Type
article
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article

Popolno barvanje, ki razlikuje točke v koronskih produktih grafov

Repository of the University of Primorsk (University of Primorska)
Graph Labeling and Dimension Problems
article

Popolno barvanje, ki razlikuje točke v koronskih produktih grafov

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Abstract

An adjacent vertex distinguishing total k-coloring f of a graph G is a proper total k-coloring of G such that no pair of adjacent vertices has the same color sets, where the color set at a vertex v, C_f^G(v), is {f(v)} ∪ {f(vu)|u ∈ V(G), vu ∈ E(G)}. In 2005 Zhang et al. posted the conjecture (AVDTCC) that every simple graph G has adjacent vertex distinguishing total (Δ(G) + 3)-coloring. In this paper we confirm the conjecture for many types of coronas, in particular for generalized, simple and l-coronas of graphs, not relating the results to particular graph classes of the factors.

Repository of the University of Primorsk (University of Primorska)
Openalex Percentile: Top 30%
Graph Labeling and Dimension Problems
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Popolno barvanje, ki razlikuje točke v koronskih produktih grafov · Repository of the University of Primorsk (University of Primorska) (2025) | TGRS Research Map | TGRS