The Connected Vertex Cover in Graphs

Authors

• Kamran Mirasheh, Department of Pure Mathematics, University of Guilan, Rasht, IranFollow
• Elham Mirashe, Department of Information Technology Management, IAU, Tehran, IranFollow
• Ebrahim Vatandoost, Department of Pure Mathematics, IKIU, Qazvin, IranFollow

Abstract

This paper presents tight bounds and characterizations for the vertex cover number and the connected vertex cover number of graphs. In particular, we identify all graphs for which βc(G) = |V (G)| − 1, proving that these are exactly the cycles and complete graphs. The analysis employs tools such as the degree matrix and the Rayleigh quotient to derive new and sharp upper bounds.

Recommended Citation

Mirasheh, Kamran; Mirashe, Elham; and Vatandoost, Ebrahim (2026) "The Connected Vertex Cover in Graphs," Theory & Applications of Graphs: Vol. 13: Iss. 1, Article 4.
Available at: https://digitalcommons.georgiasouthern.edu/tag/vol13/iss1/4