Advances and Applications in Discrete Mathematics
Volume 19, Issue 3, Pages 321 - 337
(July 2018) http://dx.doi.org/10.17654/AADMJul2018_321_337 |
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DIGIT SUMS AND VERTEX-LABELINGS
Ji Young Choi
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Abstract: For a given graph, we define a digit-sum vertex-labeling as a vertex-labeling with positive integers such that each vertex-label is the sum of digits on all the adjacent vertex-labels. We also define indispensable digits in a nonnegative integer n such that the digit sum of is 9 times the number of indispensable digits in n. Then, we show there exists a digit-sum vertex-labeling on a graph, if the degree of each vertex on the graph has one indispensable digit; or if the graph is n‑regular and has k indispensable digits for some positive integers k. |
Keywords and phrases: digit sum, casting out nines, vertex-labeling, indispensable digits. |
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