8 papers
The local antimagic (total) chromatic numbers of firecracker graphs and edge-corona product graphs
Xue Yang, Hong Bian, Xueliang Li +2
Let G=(V(G),E(G)) be a connected simple graph with n vertices and m edges. A bijection f from the edge set of G to [m] is called a local antimagic labeling of G, if for any two adj…
On Neutral Edge Sets in Anti-Ramsey Numbers
Ali Ghalavand, Qing Jie, Zemin Jin +2
The anti-Ramsey number of a graph , introduced by Erdős et al.\ in 1975, is the maximum number of colors in an edge-coloring of the complete graph that avoids a rainbow co…
On the Anti-Ramsey Number Under Edge Deletion
Ali Ghalavand, Qing Jie, Zemin Jin +2
According to a study by Erdős et al. in 1975, the anti-Ramsey number of a graph \(G\), denoted as \(AR(n, G)\), is defined as the maximum number of colors that can be used in an ed…
Intertwining local (adjacency) metric dimension with the clique number of a graph
Ali Ghalavand, Sandi Klavžar, Xueliang Li
Let be a simple connected graph with order , local metric dimension , local adjacency metric dimension , and clique number ,…
On the local metric dimension of -free graphs
Ali Ghalavand, Xueliang Li
Let \( G \) be a graph with order \( n(G) \geq 5 \), local metric dimension \( \dim_l(G) \), and clique number \( ω(G) \). In this paper, we investigate the local metric dimension…
On the local metric dimension of -free graphs
Ali Ghalavand, Sandi Klavžar, Xueliang Li
Let be a graph of order , local metric dimension , and clique number . It has been conjectured that if , then $ \dim_l…