| On Friendly Index Sets of Cyclic Silicates |
| Received:October 16, 2014 Revised:July 08, 2015 |
| Key Words:
vertex labeling friendly labeling cordiality friendly index set cycle CS$(n, m)$ arithmetic progression
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| Fund Project:Supported by the National Natural Science Foundation of China (Grant No.11371109). |
| Author Name | Affiliation | | Zhenbin GAO | College of Science, Harbin Engineering University, Heilongjiang 150001, P. R. China | | Sinmin LEE | Deptartment of Computer Science, San Jose State University, San Jose CA95192, USA | | Guangyi SUN | College of Science, Harbin Engineering University, Heilongjiang 150001, P. R. China | | Geechoon LAU | Faculty of Computer and Mathematical Sciences, Universiti Teknologi MARA (Segamat Campus), Johor 85000, Malaysia |
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| Abstract: |
| 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$(n, m)$. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2015.06.001 |
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