Total Vertex-Irregularity Labelings for Subdivision of Several Classes of Trees

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• 作者：Susilawati ; ^{nurdin@students.itb.ac.id" class="auth_mail" title="E-mail the corresponding author} ; Edy Tri Baskoro ^{ebaskoro@math.itb.ac.id" class="auth_mail" title="E-mail the corresponding author} ; Rinovia Simanjuntak ^{rino@math.itb.ac.id" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Total vertex irregularity strength ; tree ; subdivision.
• 刊名：Procedia Computer Science
• 出版年：2015
• 出版时间：2015
• 年：2015
• 卷：74
• 期：Complete
• 页码：112-117
• 全文大小：288 K

文摘

Motivated by the notion of the irregularity strength of a graph introduced by Chartrand et al. [3] in 1988 and various kind of other total labelings, Baca et al. [1] introduced the total vertex irregularity strength of a graph.

In 2010, Nurdin, Baskoro, Salman and Gaos[5] determined the total vertex irregularity strength for various types of trees, namely complete k–ary trees, a subdivision of stars, and subdivision of particular types of caterpillars. In other paper [6], they conjectured that the total vertex irregularity strength of any tree T is only determined by the number of vertices of degree 1, 2, and 3 in T . In this paper, we attempt to verify this conjecture by considering a subdivision of several types of trees, namely caterpillars, firecrackers, and amalgamation of stars.