环状硅酸盐图的友好指数集

Let G be a graph with vertex set V(G) and edge set E(G). A labeling f : V(G) →Z2 induces an edge labeling f*: E(G) → Z2 defined by f*(xy) = f(x) + f(y), for each edge xy ∈ E(G). For i ∈ Z2, let vf(i) = |{v ∈ V(G) : f(v) = i}| and ef(i) = |{e ∈ E(G) : f*(e) =i}|. A labeling f of a graph G is said to be friendly if |vf(0)- vf(1)| ≤ 1. The friendly index set of the graph G, denoted FI(G), is defined as {|ef(0)- ef(1)|: the vertex labeling f is friendly}. This is a generalization of graph cordiality. We investigate the friendly index sets of cyclic silicates CS(n, m).

On Friendly Index Sets of Cyclic Silicates

Let $G$ be a graph with vertex set $V(G)$ and edge set $E(G)$. A labeling $f : V(G)\rightarrow Z_{2}$ induces an edge labeling $ f^{*} : E(G)\rightarrow Z_{2}$ defined by $f^{*}(xy) = f(x) + f(y)$, for each edge $ xy\in E(G)$. For $i \in Z_{2}$, let $ v_{f}(i) =|\{v \in V(G) : f(v) = i\}|$ and $e_{f}(i) = |\{e\in E(G) : f^{*}(e) = i\}|$. A labeling $f$ of a graph $G$ is said to be friendly if $| v_{f}(0)-v_{f}(1) | \leq 1$. The friendly index set of the graph $G$, denoted ${\rm FI}(G)$, is defined as $\{|e_{f}(0) - e_{f}(1)|$: the vertex labeling $f$ is friendly$\}$. This is a generalization of graph cordiality. We investigate the friendly index sets of cyclic silicates CS$(n, m)$.