The closed modular chromatic number is investigated for trees and determined for several classes of trees. For each tree T in these classes, it is shown that mc ...
A coloring c of G is called a closed modular k-coloring if for every pair x, y of adjacent vertices in G either c0(x) 6= c0(y) or N[x] = N[y], in the latter ...
On Closed Modular Colorings of Trees. 415. Proposition 2.2. Let c be a closed modular coloring of a connected graph G and let u and v be false twins in G ...
The closed modular chromatic number is investigated for trees and determined for several classes of trees, showing that every tree of order 3 or more has a ...
For a positive integer k k , let c:V(G)→Zk c : V ( G ) → ℤ k be a vertex coloring where adjacent vertices may be assigned the same color.
The minimum k for which G has a closed modular k-coloring is the closed modular chromatic number mc ¯(G) of G. A rooted tree T of order at least 3 is even if ...
On closed modular colorings of rooted trees · Bryan Phinezy, Ping Zhang · Published 23 June 2013 · Mathematics · Involve, A Journal of Mathematics.
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On Closed Modular Colorings of Rooted Trees by Bryan Phinezy, Ping Zhang published in Involve, a Journal of Mathematics.
In this paper, we give a necessary and sufficient condition for a tree to have modular chromatic number 3. Keywords：trees, modular coloring, modular chromatic ...