一个路与一个完全图的直积的L(2,1)-标号
L(2,1)-Labeling of the Direct Product of a Path and a Complete Graph
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摘要:为了得到一个路P m与一个完全图K n的直积P m×K n的L(2,1)-标号数,通过归纳猜想,分类讨论,证明了m=3或4时,P m×K 3的L(2,1)-标号数为6, m≥5时,P m×K 3的L(2,1)-标号数为7, m≥5且n≥3时,P m×K n的L(2,1)-标号数的上界是3n-2Abstract:In order to obtain the L(2,1)-labeling of the direct product P m×K nof a pathP mand a complete graph K n, by means of induction, conjecture and classified discussion, the L(2,1)-labeling number of P m×K 3is determined as 6 if m=3 or 4, and the L(2,1)-labeling number of P m×K nis determined as 7 if m≥5.The upper bound of the L(2,1)-labeling number of P m×K nis shown at most m≥n-2 if m≥n-2 and n≥3
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