廣義彼得森圖的(2,1)-全標號

On (2,1)-total labelings of generalized Petersen graphs

張哲豪(Zhe-Hao Zhang)

指導教授 ： 史青林

中原大學/理學院/應用數學研究所/碩士(2012年)

https://doi.org/10.6840/cycu201200689

摘要

(p,1)-全標號是從圖中的點集合與邊集合到一個整數集合的映射，使得任兩個相鄰的點標不同的整數，任兩個相鄰的邊標不同的整數，且每一個邊與相連接的點的標號差的絕對值大於等於 p。一個(p,1)-全標號的跨度為任兩標號間的最大差。而一個圖G的所有(p,1)-全標號中的最小跨度稱為(p,1)-全標號數，寫成λ_P^T (G)。

　　令n和k為正整數，一個圖若包含點集合{u_1,…,u_n }∪{v_1,…,v_n}以及邊集合{u_i u_(i+1)|i=1,2,…,n}∪{u_i v_i |i=1,2,…,n}∪{v_i v_(i+k)|i=1,2,…,n;k

關鍵字

全標號

並列摘要

A (p,1)-total labeling of a graph G is to be an assignment of V(G)∪E(G) to integers such that any two adjacent vertices of G receive distinct integers, any two adjacent edges of G receive distinct integers and a vertex and its incident edge receive integers that differ by at least p in absolute value. The span of a (p,1)- total labeling of a graph G is the maximum difference between two labels. The minimum span of a (p,1)-total labeling of G is called the (p,1)-total number of G and denoted by λ_P^T (G).
Let n and k be two positive integers. The graph with vertex set {u_1,…,u_n }∪{v_1,…,v_n } and edges set {u_i u_(i+1) |i=1,2,…,n}∪{u_i v_i |i=1,2,…,n}∪{v_i v_(i+k) ┤|i=1,2,…,n; k

並列關鍵字

total labeling

參考文獻

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[3] D. Chen and W. Wang, (2,1)-Total labeling of outerplanar graphs, Discrete Appl. Math. 155, 2585-2593, 2007.

[4] F. C. Chi, On (2,1)-total labeling of generalized Petersen graphs, Master’s thesis of Chung Yuan Christian University, 2011.

[5] J. R. Griggs and R. K. Yeh, Labeling graphs with a condition at distance two, SIAM J. Discrete Math. 5, 586-595, 1992.