Injective Chromatic Number of Outerplanar Graphs
نویسندگان
چکیده
منابع مشابه
On the injective chromatic number of graphs
We define the concepts of an injective colouring and the injective chromatic number of a graph and give some upper and lower bounds in general, plus some exact values. We explore in particular the injective chromatic number of the hypercube and put it in the context of previous work on similar concepts, especially the theory of errorcorrecting codes. Finally, we give necessary and sufficient co...
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Let χ(G) denote the chromatic number of the square of a maximal outerplanar graph G and Q denote a maximal outerplanar graph obtained by adding three chords y1y3, y3y5, y5y1 to a 6-cycle y1y2 · · · y6y1. In this paper, it is proved that ∆+1 ≤ χ(G ) ≤ ∆+2, and χ(G) = ∆ + 2 if and only if G is Q, where ∆ represents the maximum degree of G.
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The injective chromatic number χi(G) [5] of a graph G is the minimum number of colors needed to color the vertices of G such that two vertices with a common neighbor are assigned distinct colors. In this paper we define injective chromatic sum and injective strength of a graph and obtain the injective chromatic sum of complete graph, paths, cycles, wheel graph and complete bipartite graph. We a...
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The question of whether subcubic graphs have finite packing chromatic number or not is still open although positive responses are known for some subclasses, including subcubic trees, base-3 Sierpiski graphs and hexagonal lattices. In this paper, we answer positively to the question for some subcubic outerplanar graphs. We provide asymptotic bounds depending on structural properties of the weak ...
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We give some bounds on the injective chromatic number. © 2009 Elsevier B.V. All rights reserved.
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ژورنال
عنوان ژورنال: Taiwanese Journal of Mathematics
سال: 2018
ISSN: 1027-5487
DOI: 10.11650/tjm/180807