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An $L(2,1)$-labeling of a graph $G$ is a function $f$ from the vertex set $V(G)$ to the set of all non-negative integers such that $|f(u)-f(v)|\geq 2$ if $d(u,v)=1$ and $|f(u)-f(v)|\geq 1$ if $d(u,v)=2$. The $\lambda$-number of $G$, denoted $\lambda(G)$, is the smallest number $k$ such that $G$ admits an $L(2, 1)$-labeling with $k=\max\{f(u)|u\in V(G)\}$. In this paper, we consider the square of a cycle and provide exact value for its $\lambda$-number. In addition, we also completely determine its edge span.
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참고문헌 (21)
참고문헌 신청
A. Kohl / 2006 / Knotenfarbungen mit Abstandsbedingungen / 박사 / TU Bergakademie Freiberg
D. Kor ze / 2005 / L(2; 1)-labeling of strong products of cycles / Inform. Process Lett 94 : 183 ~ 190
G.J. Chang / 1996 / The L(2; 1)-labeling problem on graphs / SIAM J. Dis-crete Math 9 : 309 ~ 316
J. van den Heuvel / 1998 / Graph labelling and radio channel assignment / J. Graph Theory 29 : 263 ~ 283
J.P. Georges / 1994 / Relating path coverings to vertex labellings with a condition at distance two / Discrete Math 135 : 103 ~ 111
D. Kor ze / 2005 / L(2; 1)-labeling of strong products of cycles / Inform. Process Lett 94 : 183 ~ 190
G.J. Chang / 1996 / The L(2; 1)-labeling problem on graphs / SIAM J. Dis-crete Math 9 : 309 ~ 316
J. van den Heuvel / 1998 / Graph labelling and radio channel assignment / J. Graph Theory 29 : 263 ~ 283
J.P. Georges / 1994 / Relating path coverings to vertex labellings with a condition at distance two / Discrete Math 135 : 103 ~ 111
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