Full Friendly Index Sets of Slender and Flat Cylinder Graphs
نویسندگان
چکیده
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 edges labeled by 0. In recent years, full friendly index sets for certain graphs were studied, such as tori, grids P2 × Pn, and cylinders Cm × Pn for some n and m. In this paper we study the full friendly index sets of cylinder graphs Cm × P2 for m ≥ 3, Cm × P3 for m ≥ 4 and C3 × Pn for n ≥ 4. The results in this paper complement the existing results in literature, so the full friendly index set of cylinder graphs are completely determined.
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 کاملLabeling Subgraph Embeddings and Cordiality of Graphs
Let $G$ be a graph with vertex set $V(G)$ and edge set $E(G)$, a vertex labeling $f : V(G)rightarrow mathbb{Z}_2$ induces an edge labeling $ f^{+} : E(G)rightarrow mathbb{Z}_2$ defined by $f^{+}(xy) = f(x) + f(y)$, for each edge $ xyin E(G)$. For each $i in mathbb{Z}_2$, let $ v_{f}(i)=|{u in V(G) : f(u) = i}|$ and $e_{f^+}(i)=|{xyin E(G) : f^{+}(xy) = i}|$. A vertex labeling $f$ of a graph $G...
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 کاملConjugate Heat Transfer of MHD non-Darcy Mixed Convection Flow of a Nanofluid over a Vertical Slender Hollow Cylinder Embedded in Porous Media
In this paper, conjugate heat transfer of magneto hydrodynamic mixed convection of nanofluid about a vertical slender hollow cylinder embedded in a porous medium with high porosity have been numerically studied. The Forchheimer’s modification of Darcy’s law was used in representing the nanofluid motion inside the porous media. The governing boundary layer equations were transformed to non-dimen...
متن کاملOn vertex balance index set of some graphs
Let Z2 = {0, 1} and G = (V ,E) be a graph. A labeling f : V → Z2 induces an edge labeling f* : E →Z2 defined by f*(uv) = f(u).f (v). For i ε Z2 let vf (i) = v(i) = card{v ε V : f(v) = i} and ef (i) = e(i) = {e ε E : f*(e) = i}. A labeling f is said to be Vertex-friendly if | v(0) − v(1) |≤ 1. The vertex balance index set is defined by {| ef (0) − ef (1) | : f is vertex-friendly}. In this paper ...
متن کامل