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

Abstract

Abstract 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.