Results 31 to 40 of about 41,334 (304)
Total Coloring of Dumbbell Maximal Planar Graphs
Mathematics, 2022 The Total Coloring Conjecture (TCC) states that every simple graph G is totally (Δ+2)-colorable, where Δ denotes the maximum degree of G. In this paper, we prove that TCC holds for dumbbell maximal planar graphs.
Yangyang Zhou +3 more
doaj +1 more source
Neighbor Distinguishing Colorings of Graphs with the Restriction for Maximum Average Degree
Axioms, 2023 Neighbor distinguishing colorings of graphs represent powerful tools for solving the channel assignment problem in wireless communication networks. They consist of two forms of coloring: neighbor distinguishing edge coloring, and neighbor distinguishing ...
Jingjing Huo +3 more
doaj +1 more source
Total dominator total coloring of a graph
Contributions to Discrete Mathematics, 2023 Here, we initiate to study the total dominator total coloring of a graph which is a total coloring of the graph such that each object of the graph is adjacent or incident to every object of some color class. In more details, while in section 2 we present some tight lower and upper bounds for the total dominator total chromatic number of a graphs in ...
Kazemi, Adel P. +2 more
openaire +2 more sources
On a Total Version of 1-2-3 Conjecture
Discussiones Mathematicae Graph Theory, 2020 A total k-coloring of a graph G is a coloring of vertices and edges of G using colors of the set {1, . . . , k}. These colors can be used to distinguish adjacent vertices of G. There are many possibilities of such a distinction.
Baudon Olivier +5 more
doaj +1 more source
Neighbor sum distinguishing total choice number of IC-planar graphs with restrictive conditions
AIMS Mathematics, 2023 A neighbor sum distinguishing (NSD) total coloring $ \phi $ of $ G $ is a proper total coloring such that $ \sum_{z\in E_{G}(u)\cup\{u\}}\phi(z)\neq\sum_{z\in E_{G}(v)\cup\{v\}}\phi(z) $ for each edge $ uv\in E(G) $.
Fugang Chao , Donghan Zhang
doaj +1 more source
On (p, 1)-Total Labelling of Some 1-Planar Graphs
Discussiones Mathematicae Graph Theory, 2021 A graph is 1-planar if it can be drawn on the plane so that each edge is crossed by at most one other edge. In this paper, it is proved that the (p, 1)-total labelling number (p ≥ 2) of every 1-planar graph G is at most Δ(G) + 2p − 2 provided that Δ (G) ≥
Niu Bei, Zhang Xin
doaj +1 more source
Total Global Dominator Coloring of Trees and Unicyclic Graphs
مجلة بغداد للعلوم, 2023 A total global dominator coloring of a graph is a proper vertex coloring of with respect to which every vertex in dominates a color class, not containing and does not dominate another color class.
Chithra K. P., Joseph Mayamma
doaj +1 more source
Generalized Fractional Total Colorings of Complete Graph
Discussiones Mathematicae Graph Theory, 2013 An additive and hereditary property of graphs is a class of simple graphs which is closed under unions, subgraphs and isomorphism. Let P and Q be two additive and hereditary graph properties and let r, s be integers such that r ≥ s Then an fractional (P,
Karafová Gabriela
doaj +1 more source
Neighbor Product Distinguishing Total Colorings of Planar Graphs with Maximum Degree at least Ten
Discussiones Mathematicae Graph Theory, 2021 A proper [k]-total coloring c of a graph G is a proper total coloring c of G using colors of the set [k] = {1, 2, . . . , k}. Let p(u) denote the product of the color on a vertex u and colors on all the edges incident with u.
Dong Aijun, Li Tong
doaj +1 more source
PEWARNAAN TITIK TOTAL SUPER ANTI-AJAIB LOKAL PADA GRAF PETERSEN DIPERUMUM P(n,k) DENGAN k=1,2
Barekeng, 2021 The local antimagic total vertex labeling of graph G is a labeling that every vertices and edges label by natural number from 1 to such that every two adjacent vertices has different weights, where is The sum of a vertex label and the labels of all ...
Deddy Setyawan +4 more
doaj +1 more source