Graceful, Harmonious and Magic Type Labelings by Susana C. López & Francesc A. Muntaner-Batle
Author:Susana C. López & Francesc A. Muntaner-Batle
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham
Figures 5.7 and 5.8 illustrate examples of the previous definitions.
Fig. 5.7A tree with an even degree sequence and even diameter
Fig. 5.8A tree with a quasi even degree sequence and odd diameter
Theorem 5.4 ([10])
Every tree with an even or quasi even degree sequence is graceful.
In order to prove Theorem 5.4, we introduce the following results. The first one establishes a relation between the size and the diameter of a tree with a (quasi) even degree sequence.
Lemma 5.3 ([10])
Let T be a tree of size m and even diameter D. If T has an even degree sequence, then m + D∕2 is even. If T has a quasi even degree sequence, then m + D∕2 is odd.
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