Results 251 to 260 of about 1,402,601 (292)
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Neighbor sum distinguishing total chromatic number of planar graphs
Applied Mathematics and Computation, 2018Let G = (V(G), E(G)) be a graph and ϕ be a proper k-total coloring of G. Set fϕ(v)=∑uv∈E(G)ϕ(uv)+ϕ(v), for each v ∈ V(G). If fϕ(u) ≠ fϕ(v) for each edge uv ∈ E(G), the coloring ϕ is called a k-neighbor sum distinguishing total coloring of G. The smallest
Changqing Xu, Jianguo Li, Shan Ge
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Total Dominator Total Chromatic Numbers of Some Graphs
Utilitas MathematicaTotal dominator total coloring of a graph 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. The minimum namber of the color classes of a total dominator total coloring of a graph is called the total dominator total chromatic number of the graph.
Vusuqi, Leila +2 more
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The total chromatic numbers of joins of sparse graphs [PDF]
Australas. J Comb., 2003 A total colouring of a graph \(G= (V,E)\) is a map of \(V\cup E\) into a set \(C\) (of colours) such that adjacent or incident elements receive different colours; the total chromatic number \(\chi''(G)\) of \(G\) is the minimum cardinality of \(C\) which allows such a mapping.
Anthony J. W. Hilton +2 more
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k-tuple total dominator chromatic number and Mycielskian graphs
Georgian Mathematical JournalThe k-tuple total dominator chromatic number is a graph parameter that measures the minimum number of colors required for a proper coloring, where each vertex must be adjacent to every vertex of k distinct color classes. In this paper, we investigate the
Walid Marweni
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Asymptotics of the total chromatic number for multigraphs [PDF]
Australas. J Comb., 1999 Let \(\chi(G)\) and \(\chi^*(G)\) be the total chromatic number and its fractional analogue of a multigraph \(G\), respectively. This article shows that for any \(\varepsilon> 0\), there exists \(D= D(\varepsilon)\) such that every multigraph \(G\) with \(\chi^*(G)> D\) satisfies \[ (1+ \varepsilon)^{-1}< {\chi(G)\over\chi^*(G)}< 1+ \varepsilon, \] i.e.
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International Journal of Computer Mathematics Computer Systems Theory
Graph coloring is a core concept in graph theory, which has an extensive application in the field of computer science and engineering. Graph elements can be colored based on constraints like degree, adjacency or distance; geo coloring uses the concept of
V. Ponsathya +4 more
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Graph coloring is a core concept in graph theory, which has an extensive application in the field of computer science and engineering. Graph elements can be colored based on constraints like degree, adjacency or distance; geo coloring uses the concept of
V. Ponsathya +4 more
semanticscholar +1 more source
An Improvement of Hind's Upper Bound on the Total Chromatic Number
Combinatorics, Probability and Computing, 1996We show that the total chromatic number of a simple k-chromatic graph exceeds the chromatic index by at most 18k ⅓ log ½ 3k.
Amanda G. Chetwynd, Roland Häggkvist
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Results about the total chromatic number and the conformability of some families of circulant graphs
Discrete Applied Mathematics, 2023L. Faria +3 more
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Total chromatic number for certain classes of product graphs
Discret. Math. Algorithms Appl., 2023T. Sandhiya, J. Geetha, K. Somasundaram
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Total chromatic number of S-valued graphs
RECENT TRENDS IN SCIENCE AND ENGINEERING, 2022A. Devi +2 more
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