منابع مشابه
Full friendly index sets of cylinder graphs
Let G = (V,E) be a connected simple graph. A labeling f : V → Z2 induces an edge labeling f : E → Z2 defined by f(xy) = f(x) + f(y) for each xy ∈ E. For i ∈ Z2, let vf (i) = |f−1(i)| and ef(i) = |(f+)−1(i)|. A labeling f is called friendly if |vf (1) − vf(0)| ≤ 1. For a friendly labeling f of a graph G, we define the friendly index of G under f by if(G) = ef (1) − ef(0). The set {if(G) | f is a...
متن کاملFull friendly index sets of P2×Pn
LetG=(V ,E) be a graph, a vertex labeling f : V → Z2 induces an edge labeling f ∗ : E → Z2 defined by f ∗(xy)=f (x)+f (y) for each xy ∈ E. For each i ∈ Z2, define vf (i)=|f−1(i)| and ef (i)=|f ∗−1(i)|. We call f friendly if |vf (1)− vf (0)| 1. The full friendly index set of G is the set of all possible values of ef (1)− ef (0), where f is friendly. In this note, we study the full friendly index...
متن کاملThe Friendly Index Set of Pm × Pn
For a graph G = (V,E) and a binary labeling (coloring) f : V (G) → Z2, let vf (i) = |f−1(i)|. f is said to be friendly if |vf (1) − vf (0)| ≤ 1. The labeling f : V (G) → Z2 induces an edge labeling f∗ : E(G) → Z2 defined by f∗(xy) = |f(x)− f(y)| ∀xy ∈ E(G). 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 ...
متن کاملFull Edge-friendly Index Sets of Complete Bipartite Graphs
Let G = (V,E) be a simple graph. An edge labeling f : E → {0, 1} induces a vertex labeling f : V → Z2 defined by f(v) ≡ ∑ uv∈E f(uv) (mod 2) for each v ∈ V , where Z2 = {0, 1} is the additive group of order 2. For i ∈ {0, 1}, let ef (i) = |f−1(i)| and vf (i) = |(f+)−1(i)|. A labeling f is called edge-friendly if |ef (1) − ef (0)| ≤ 1. If (G) = vf (1) − vf (0) is called the edge-friendly index o...
متن کاملFull Friendly Index Sets of Slender and Flat Cylinder Graphs
Let G = (V, E) be a connected simple graph. A labeling f : V → Z2 induces an edge labeling f∗ : E → Z2 defined by f∗(xy) = f(x) + f(y) for each xy ∈ E. For i ∈ Z2, let vf (i) = |f−1(i)| and ef (i) = |f∗−1(i)|. A labeling f is called friendly if |vf (1)− vf (0)| ≤ 1. The full friendly index set of G consists all possible differences between the number of edges labeled by 1 and the number of edge...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2013
ISSN: 0166-218X
DOI: 10.1016/j.dam.2012.10.028