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Spectra of total graphs

Discrete Applied Mathematics, 2023
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Tianyi Bu, Shaobin Huang
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TENACITY OF TOTAL GRAPHS

International Journal of Foundations of Computer Science, 2014
Communication networks must be constructed to be as stable as possible, not only with the respect to the initial disruption, but also with respect to the possible reconstruction. Many graph theoretical parameters have been used to describe the stability of communication networks.
Yinkui Li   +3 more
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Total domination in graphs

Networks, 1980
AbstractA set D of vertices of a finite, undirected graph G = (V, E) is a total dominating set if every vertex of V is adjacent to some vertex of D. In this paper we initiate the study of total dominating sets in graphs and, in particular, obtain results concerning the total domination number of G (the smallest number of vertices in a total dominating ...
Ernest J. Cockayne   +2 more
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Total matchings and total coverings of graphs

Journal of Graph Theory, 1977
AbstractIn graph theory, the related problems of deciding when a set of vertices or a set of edges constitutes a maximum matching or a minimum covering have been extensively studied. In this paper we generalize these ideas by defining total matchings and total coverings, and show that these sets, whose elements in general consist of both vertices and ...
Yousef Alavi   +3 more
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Total Colourings of Graphs

Bulletin of the London Mathematical Society, 1989
We prove that the TCC (Total Colouring Conjecture) is true for complete r-partite graphs which extends a result of M. Rosenfeld. We also give an alternate, slightly simpler proof of an earlier result (which says that the TCC is true for graphs having maximum degree 3) obtained independently by M. Rosenfeld and N. Vijayaditya.
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Total Colorings of Degenerated Graphs

Combinatorica, 2001
A total coloring of a graph G is a coloring of all elements of G, i.e. vertices and edges, such that no two adjacent or incident elements receive the same color. A graph G is s-degenerate for a positive integer s if G can be reduced to a trivial graph by successive removal of vertices with degree ≤s.
Shuji Isobe   +2 more
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Girth and Total Domination in Graphs

Graphs and Combinatorics, 2011
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Michael A. Henning, Anders Yeo
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