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1
Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik
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On the cost chromatic number of outerplanar, planar, and line graphs

100%
Mitchem J., Morriss P., Schmeichel E.
Discussiones Mathematicae Graph Theory
|
1997
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tom 17
|
nr 2
229-241
EN
We consider vertex colorings of graphs in which each color has an associated cost which is incurred each time the color is assigned to a vertex. The cost of the coloring is the sum of the costs incurred at each vertex. The cost chromatic number of a graph with respect to a cost set is the minimum number of colors necessary to produce a minimum cost coloring of the graph. We show that the cost chromatic number of maximal outerplanar and maximal planar graphs can be arbitrarily large and construct several infinite classes of counterexamples to a conjecture of Harary and Plantholt on the cost chromatic number of line graphs.
2
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Hamilton decompositions of line graphs of some bipartite graphs

100%
Pike D.
Discussiones Mathematicae Graph Theory
|
2005
|
tom 25
|
nr 3
303-310
EN
Some bipartite Hamilton decomposable graphs that are regular of degree δ ≡ 2 (mod 4) are shown to have Hamilton decomposable line graphs. One consequence is that every bipartite Hamilton decomposable graph G with connectivity κ(G) = 2 has a Hamilton decomposable line graph L(G).
3
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On some characterizations of strong power graphs of finite groups

88%
Bhuniya A. K., Bera S.
Special Matrices
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2016
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tom 4
|
nr 1
121-129
EN
Let G be a finite group of order n. The strong power graph Ps(G) of G is the undirected graph whose vertices are the elements of G such that two distinct vertices a and b are adjacent if am1=bm2 for some positive integers m1, m2 < n. In this article we classify all groups G for which Ps(G) is a line graph. Spectrum and permanent of the Laplacian matrix of the strong power graph Ps(G) are found for any finite group G.
4
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Clique irreducibility of some iterative classes of graphs

88%
Aparna Lakshmanan S., Vijayakumar A.
Discussiones Mathematicae Graph Theory
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2008
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tom 28
|
nr 2
307-321
EN
In this paper, two notions, the clique irreducibility and clique vertex irreducibility are discussed. A graph G is clique irreducible if every clique in G of size at least two, has an edge which does not lie in any other clique of G and it is clique vertex irreducible if every clique in G has a vertex which does not lie in any other clique of G. It is proved that L(G) is clique irreducible if and only if every triangle in G has a vertex of degree two. The conditions for the iterations of line graph, the Gallai graphs, the anti-Gallai graphs and its iterations to be clique irreducible and clique vertex irreducible are also obtained.
5
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Edge-Transitivity of Cayley Graphs Generated by Transpositions

75%
Ganesan A.
Discussiones Mathematicae Graph Theory
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2016
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tom 36
|
nr 4
1035-1042
EN
Let S be a set of transpositions generating the symmetric group Sn (n ≥ 5). The transposition graph of S is defined to be the graph with vertex set {1, . . . , n}, and with vertices i and j being adjacent in T(S) whenever (i, j) ∈ S. In the present note, it is proved that two transposition graphs are isomorphic if and only if the corresponding two Cayley graphs are isomorphic. It is also proved that the transposition graph T(S) is edge-transitive if and only if the Cayley graph Cay(Sn, S) is edge-transitive.
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