Let G=(V,E) be a graph with vertex set V and edge set E. A local antimagic total vertex coloring f of a graph G with vertex-set V and edge-set E is an injective map from V∪E to {1,2,…,|V|+|E|} such that if for each uv∈E(G) then w(u)≠w(v), where w(u)=∑uv∈E(G)f(uv)+f(u). If the range set f satisfies f(V)={1,2,…,|V|}, then the labeling is said to be local super antimagic total labeling. This labeling generates a proper vertex coloring of the graph G with the color w(v) assigning the vertex v. The local super antimagic total chromatic number of graph G, χlsat(G) is defined as the least number of colors that are used for all colorings generated by the local super antimagic total labeling of G. In this paper we investigate the existence of the local super antimagic total chromatic number for some particular classes of graphs such as a tree, path, cycle, helm, wheel, gear, sun, and regular graphs as well as an amalgamation of stars and an amalgamation of wheels.

This study aimed to describe the mathematical connections process of students in solving geometry problems. The mathematical connections process was the students' steps in doing mathematical connections. The observed aspects were the internal connections (the interrelationships between mathematical concepts) and external connections (the mathematical interrelationships and outside of mathematics or daily life). The samples of this reasearch were the student with high and low mathematical logical intelligence. The results of the research showed that the students with high logical mathematical intelligence did the internal and external connections in solving geometry problems completely based on polya problem solving steps. Meanwhile, the students with low logical mathematical intelligence did the internal and external connections until the step of understanding the problems.

Let G be a connected graph with vertex set

<abstract><p>The local metric dimension is one of many topics in graph theory with several applications. One of its applications is a new model for assigning codes to customers in delivery services. Let $ G $ be a connected graph and $ V(G) $ be a vertex set of $ G $. For an ordered set $ W = \{ x_1, x_2, \ldots, x_k\} \subseteq V(G) $, the representation of a vertex $ x $ with respect to $ W $ is $ r_G(x|W) = \{(d(x, x_1), d(x, x_2), \ldots, d(x, x_k) \} $. The set $ W $ is said to be a local metric set of $ G $ if $ r(x|W)\neq r(y|W) $ for every pair of adjacent vertices $ x $ and $ y $ in $ G $. The eccentricity of a vertex $ x $ is the maximum distance between $ x $ and all other vertices in $ G $. Among all vertices in $ G $, the smallest eccentricity is called the radius of $ G $ and a vertex whose eccentricity equals the radius is called a central vertex of $ G $. In this paper, we developed a new concept, so-called the central local metric dimension by combining the concept of local metric dimension with the central vertex of a graph. The set $ W $ is a central local metric set if $ W $ is a local metric set and contains all central vertices of $ G $. The minimum cardinality of a central local metric set is called a central local metric dimension of $ G $. In the main result, we introduce the definition of the central local metric dimension of a graph and some properties, then construct the central local metric dimensions for trees and establish results for the grid graph.</p></abstract>

, is the number of vertices in a basis of . In general, the comb product and the corona product are noncommutative operations in a graph. However, these operations can be commutative with respect to the metric dimension for some graphs with certain conditions. In this paper, we determine the metric dimension of the generalized comb and corona products of graphs and the necessary and sufficient conditions of the graphs in order for the comb and corona products to be commutative operations with respect to the metric dimension.