On Friendly Index Sets of Trees
نویسندگان
چکیده
For a graph G = (V, E) and a coloring f : V (G) → Z 2 let vf (i) = |f−1(i)|. f is said to be friendly if |vf (1)−vf (0)| ≤ 1. The coloring f : V (G) → Z 2 induces an edge labeling f∗ : E(G) → Z 2 defined by f∗(xy) = f(x) + f(y) ∀xy ∈ E(G), where the summation is done in Z 2. Let ef (i) = |f∗−1(i)|. The friendly index set of the graph G, denoted by FI(G), is defined by FI(G) = {|ef (1)− ef (0)| : f is a friendly vertx labeling of G }. In this paper we will determine the friendly index set of certain classes of trees, which in turn will verify the validity of the conjecture that the elements of friendly index set of any tree form an arithmetic progression.
منابع مشابه
On a Conjecture Concerning the Friendly Index Sets of Trees
For a graph G = (V,E) and a binary labeling f : V (G) → Z2, let vf (i) = |f−1(i)|. The labling f is said to be friendly if |vf (1)−vf (0)| ≤ 1. Any vertex labeling f : V (G) → Z2 induces an edge labeling f∗ : E(G) → Z2 defined by f∗(xy) = |f(x)− f(y)|. Let ef (i) = |f∗−1(i)|. The friendly index set of the graph G, denoted by FI(G), is defined by FI(G) = {|ef (1)− ef (0)| : f is a friendly verte...
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تاریخ انتشار 2007