The graph is a pair of sets , where finite set whose elements are called vertices, and the pairs members . which edge. Let be simple distance between points denoted by length shortest path Given there vertex on connected then If -partition representation with respect to -ordered pairs, for all different, partition dimension partition. minimal -number -differentiating In this study, dimensions s...

A Hamiltonian cycle (path) of a graph G is a simple cycle (path) which contains all the vertices of G. The Hamiltonian cycle problem asks whether a given graph contains a Hamiltonian cycle. It is NP-complete even for 3-connected planar graphs [3, 61. However, the problem becomes polynomial-time solvable for Cconnected planar graphs: Tutte proved that such a graph necessarily contains a Hamilton...

mean labelings are a type of additive vertex labeling. this labeling assigns non-negative integers to the vertices of a graph in such a way that all edge-weights are different, where the weight of an edge is defined as the mean of the end-vertex labels rounded up to the nearest integer. in this paper we focus on mean labelings of some graphs that are the result of the corona operation. in parti...