Infinitely Many Trees with Maximum Number of Holes Zero, One, and Two

Srinivasa Rao Kola, Balakrishna Gudla and P. K. Niranjan

Journal of Applied Mathematics, 2018, vol. 2018, issue 1

Abstract: An L(2,1)‐coloring of a simple connected graph G is an assignment f of nonnegative integers to the vertices of G such that |f(u) − f(v)|⩾2 if d(u, v) = 1 and |f(u) − f(v)|⩾1 if d(u, v) = 2 for all u, v ∈ V(G), where d(u, v) denotes the distance between u and v in G. The span of f is the maximum color assigned by f. The span of a graph G, denoted by λ(G), is the minimum of span over all L(2,1)‐colorings on G. An L(2,1)‐coloring of G with span λ(G) is called a span coloring of G. An L(2,1)‐coloring f is said to be irreducible if there exists no L(2,1)‐coloring g such that g(u) ⩽ f(u) for all u ∈ V(G) and g(v)

Date: 2018
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https://doi.org/10.1155/2018/8186345

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnljam:v:2018:y:2018:i:1:n:8186345

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