http://chineseinput.net/에서 pinyin(병음)방식으로 중국어를 변환할 수 있습니다.
변환된 중국어를 복사하여 사용하시면 됩니다.
RADIO LABELING AND RADIO NUMBER FOR GENERALIZED CATERPILLAR GRAPHS
NAZEER, SAIMA,KHAN, M. SAQIB,KOUSAR, IMRANA,NAZEER, WAQAS The Korean Society for Computational and Applied M 2016 Journal of applied mathematics & informatics Vol.34 No.5
A Radio labeling of the graph G is a function g from the vertex set V (G) of G to ℤ<sup>+</sup> such that |g(u) - g(v)| ≥ diam(G) + 1 - d<sub>G</sub>(u, v), where diam(G) and d(u, v) are diameter and distance between u and v in graph G respectively. The radio number rn(G) of G is the smallest number k such that G has radio labeling with max{g(v) : v ∈ V(G)} = k. We investigate radio number for some families of generalized caterpillar graphs.
Radio labeling and Radio Number For Generalized Caterpillar Graphs
Saima Nazeer,M. Saqib Khan,Imrana Kausar,Waqas Nazeer 한국전산응용수학회 2016 Journal of applied mathematics & informatics Vol.34 No.5
A Radio labeling of the graph $G$ is a function $g$ from the vertex set $V(G)$ of $G$ to $\mathbb{Z}^{+}$ such that $|g(u)-g(v)|\geq\text{diam}(G)+1-d_G(u,v)$, where diam$(G)$ and $d(u,v)$ are diameter and distance between $u$ and $v$ in graph $G$ respectively. The radio number rn$(G)$ of $G$ is the smallest number $k$ such that $G$ has radio labeling with max$\{g(v):v\in V(G)\}=k$. We investigate radio number for some families of generalized caterpillar graphs.
RADIO AND RADIO ANTIPODAL LABELINGS FOR CIRCULANT GRAPHS G(4k + 2; {1, 2})
Nazeer, Saima,Kousar, Imrana,Nazeer, Waqas The Korean Society for Computational and Applied M 2015 Journal of applied mathematics & informatics Vol.33 No.1
A radio k-labeling f of a graph G is a function f from V (G) to $Z^+{\cup}\{0\}$ such that $d(x,y)+{\mid}f(x)-f(y){\mid}{\geq}k+1$ for every two distinct vertices x and y of G, where d(x, y) is the distance between any two vertices $x,y{\in}G$. The span of a radio k-labeling f is denoted by sp(f) and defined as max$\{{\mid}f(x)-f(y){\mid}:x,y{\in}V(G)\}$. The radio k-labeling is a radio labeling when k = diam(G). In other words, a radio labeling is an injective function $f:V(G){\rightarrow}Z^+{\cup}\{0\}$ such that $${\mid}f(x)=f(y){\mid}{\geq}diam(G)+1-d(x,y)$$ for any pair of vertices $x,y{\in}G$. The radio number of G denoted by rn(G), is the lowest span taken over all radio labelings of the graph. When k = diam(G) - 1, a radio k-labeling is called a radio antipodal labeling. An antipodal labeling for a graph G is a function $f:V(G){\rightarrow}\{0,1,2,{\ldots}\}$ such that $d(x,y)+{\mid}f(x)-f(y){\mid}{\geq}diam(G)$ holds for all $x,y{\in}G$. The radio antipodal number for G denoted by an(G), is the minimum span of an antipodal labeling admitted by G. In this paper, we investigate the exact value of the radio number and radio antipodal number for the circulant graphs G(4k + 2; {1, 2}).
Radio and Radio Antipodal Labelings For Circulant Graphs
Saima Nazeer,Imrana Kousar,Waqas Nazeer 한국전산응용수학회 2015 Journal of applied mathematics & informatics Vol.33 No.1
A radio $k$-labeling $f$ of a graph $G$ is a function $f$ from $V(G)$ to $Z^{+}\cup\{0\}$ such that$d(x,y)+|f(x)-f(y)|\geq k+1$ for every two distinct vertices $x$ and $y$ of $G$, where $d(x,y)$ is the distance between any two vertices $x, y\in G$. The span of a radio $k$-labeling $f$ is denoted by $sp(f)$ and defined as max$\{|f(x)-f(y)|: x,y\in V(G)\}$. The radio $k$-labeling is a radio labeling when$k=\text{diam}(G)$. In other words, a radio labeling is an injective function $f:V(G)\rightarrow Z^{+}\cup\{0\}$ such that$$|f(x)-f(y)|\geq \text{diam}(G)+1-d(x,y)$$ for any pair of vertices $x, y \in G$. The radio number of $G$denoted by rn$(G)$, is the lowest span taken over all radio labelings of the graph. When $k=\text{diam}(G)-1$, a radio $k$- labeling is called a radioantipodal labeling. An antipodal labeling for a graph $G$ is a function $f:V(G)\rightarrow\{0, 1, 2, ...\}$such that $d(x,y)+|f(x)-f(y)|\geq \text{diam}(G)$ holds for all $x,y\in G$. The radio antipodal number for $G$ denoted by an$(G)$, is the minimum span of an antipodal labeling admitted by $G$. In this paper, we investigate the exact value of the radio number and radio antipodal number for thecirculant graphs $G(4k+2;\{1,2\})$.