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(2,1)-TOTAL NUMBER OF JOINS OF PATHS AND CYCLES

Weifan Wang, Jing Huang, Sun Haina and Danjun Huang
Taiwanese Journal of Mathematics
Vol. 16, No. 2 (April 2012), pp. 605-619
Stable URL: http://www.jstor.org/stable/taiwjmath.16.2.605
Page Count: 15
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(2,1)-TOTAL NUMBER OF JOINS OF PATHS AND CYCLES
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Abstract

Abstract The (2,1)-total number λ2t(G) of a graph G is the width of the smallest range of integers that suffices to label the vertices and edges of G such that no two adjacent vertices or two adjacent edges have the same label and the difference between the label of a vertex and its incident edges is at least 2. In this paper, we characterize completely the (2,1)-total number of the join of two paths and the join of two cycles. 2010 Mathematics Subject Classification: 05C15. Key words and phrases: (2,1)-Total number, Path, Cycle, Join, Maximum degree.

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