Matching-Type Image-Labelings of Trees

Abstract

A variety of labelings on trees have emerged in order to attack the Graceful Tree Conjecture, but lack showing the connections between two labelings. In this paper, we propose two new labelings: vertex image-labeling and edge image-labeling, and combine new labelings to form matching-type image-labeling with multiple restrictions. The research starts from the set-ordered graceful labeling of the trees, and we give several generation methods and relationships for well-known labelings and two new labelings on trees.

Generalized Arithmetic Staircase Graphs and Their Total Edge Irregularity Strengths

“…According to [8], regarding the application side, graph theory plays a vital role as it is at the foundations, for instance, of the internet, parallel computing, distributed computing, molecular topology, dynamics, energy, electricity, and electronic circuit design. Among many subjects in graph theory, labeling is one that is also continuing to develop for both undirected and directed graphs (see [9][10][11][12][13][14]). In addition, labeling itself is also playing an important role in many fields, such as coding theory, physics, astronomy, circuit design, and computer science (see [15]).…”