10 papers
Anti-Ramsey Numbers for Spanning Linear Forests of 3-Vertex Paths and Matchings
Ali Ghalavand, Xueliang Li
A subgraph in an edge-colored graph is called rainbow if all its edges have distinct colors. For a graph and an integer , the anti-Ramsey number is the maximum num…
On Neutral Edge Sets in Anti-Ramsey Numbers
Ali Ghalavand, Qing Jie, Zemin Jin +2
The anti-Ramsey number of a graph , introduced by ErdÅs et al.\ in 1975, is the maximum number of colors in an edge-coloring of the complete graph that avoids a rainbow c…
On the Anti-Ramsey Number Under Edge Deletion
Ali Ghalavand, Qing Jie, Zemin Jin +2
According to a study by ErdÅs 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 e…
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 \( Ï(G) \). In this paper, we investigate the local metric dimension…
On Maximum Induced Forests of the Balanced Bipartite Graphs
Ali Ghalavand, Xueliang Li
The decycling number of a graph is the minimum number of vertices that must be removed to eliminate all cycles in . The forest number is the maximum numbe…
On a Conjecture about Comparing the First and Second Zagreb Indices of Graphs
Ali Ghalavand
Let be a graph with order , size , first Zagreb index , and second Zagreb index . More than twenty years ago, it was conjectured that $\frac{M_1(G)}…