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On Total Chromatic Number of Complete Multipartite Graphs
Discrete Applied MathematicszbMATH Open Web Interface contents unavailable due to conflicting licenses.
Aseem Dalal, B. S. Panda 0001
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Total chromatic number of honeycomb network
Journal of Discrete Mathematical Sciences and Cryptography, 2020AbstractThe total coloring of a graph G is defined as assigning colors to the set of vertices and set of edges of G so that any adjacent or incident elements of G receive different colors.
S. Shyama, M. R. Chithra
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Journal of Discrete Mathematical Sciences and Cryptography, 2015
AbstractUsing Lotker's interlacing theorem on the Laplacian eigenvalues of a graph in [3] and Wang and Belardo's interlacing theorem on the signless Laplacian eigenvalues of a graph in [4], we obtain inequalities which involve the independence number, chromatic number, Laplacian eigenvalues, and signless Laplacian eigenvalues of a graph.
Rao Li
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AbstractUsing Lotker's interlacing theorem on the Laplacian eigenvalues of a graph in [3] and Wang and Belardo's interlacing theorem on the signless Laplacian eigenvalues of a graph in [4], we obtain inequalities which involve the independence number, chromatic number, Laplacian eigenvalues, and signless Laplacian eigenvalues of a graph.
Rao Li
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Inclusion total chromatic number
Discrete Mathematics, 2021zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Determining equitable total chromatic number for infinite classes of complete r-partite graphs
Discrete Applied Mathematics, 2020An equitable total coloring is the assignment of colors to the edges and vertices of a graph G so that incident and adjacent elements receive different colors, and the difference between the cardinalities of any two color classes is either 0 or 1.
Anderson G. da Silva +2 more
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Circular total chromatic numbers of graphs
Discrete Mathematics, 2016zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Cheyu Lin, Xuding Zhu
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On the double total dominator chromatic number of graphs
Discrete Mathematics, Algorithms and Applications, 2021In this paper, we introduce and study a new coloring problem of graphs called the double total dominator coloring. A double total dominator coloring of a graph [Formula: see text] with minimum degree at least 2 is a proper vertex coloring of [Formula: see text] such that each vertex has to dominate at least two color classes.
Fairouz Beggas +2 more
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Total-chromatic number and chromatic index of dually chordal graphs
Information Processing Letters, 1999Abstract Given a graph G and a vertex v , a vertex u∈N(v) is a maximum neighbor of v if for all w∈N(v) we have N(w)⫅N(u) , where N(v) denotes the neighborhood of v in G . A maximum neighborhood elimination order of G is a linear order v 1 ,v 2 ,…,v n on its vertex set ...
Celina M. H. de Figueiredo +2 more
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Complementary Graphs and Total Chromatic Numbers
SIAM Journal on Applied Mathematics, 1974A theorem of the Nordhaus–Gaddum class is obtained for the total chromatic number of a graph and its complement.
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An upper bound for the total chromatic number
Graphs and Combinatorics, 1990The chromatic number, the edge chromatic number, and the total chromatic number of a graph H are respectively denoted by \(\chi\) (H), \(\chi '(H)\), and \(\chi ''(H)\). Theorem: For any graph H, \(\chi ''(H)\leq \chi '(H)+2\lceil \sqrt{\chi (H)}\rceil.\) Let \(\Delta\) (H) be the maximum degree of graph H.
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