2025/08/03 by Kamal Santra, Pandey, Arti, Santra, Kamal · 1 citation
Computer Science · Mathematics · #Advanced Graph Theory Research #Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Interconnection Networks and Systems #Limits and Structures in Graph Theory
paper · pdf · doi:10.48550/arxiv.2508.01935
openalex publication_date 2025/08/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let G=(V, E) be a graph where V(G) and E(G) are the vertex and edge sets, respectively. In a graph G, two edges e1, e2∈ E(G) are said to have common edge e≠ e1, e2 if e joins an endpoint of e1 to an endpoint of e2 in G. A subset D⊆ E(G) is called an edge open packing set in G if no two edges in D share a common edge in G, and the largest size of such a set in G is known as edge open packing number, represented by ρeo(G). In the introductory paper (Chelladurai et al. (2022)), necessary and sufficient conditions for ρeo(G)=1, 2 were provided, and the graphs G with ρeo(G)∈ \m-2, m-1, m\ were characterized, where m is the number of edges of G. In this paper, we further characterize the graphs G. First, we show necessary and sufficient conditions for ρeo(G)=t, for any integer t≥ 3. Finally, we characterize the graphs with ρeo(G)=m-3.