On sufficient conditions for $k$-leaf-connected graphs
Received:December 17, 2023  Revised:February 20, 2024
Key Words: $k$-leaf-connected, Zagreb index, Hyper-Zagreb index  
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Author NameAffiliationAddress
Guoyan Ao Hulunbuir University 内蒙古自治区呼伦贝尔市海拉尔区成吉思汗中路26号
Xia Hong* Luoyang Normal University 河南省洛阳市伊滨区吉庆路6号洛阳师范学院
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      For any integer $k\geq2,$ a graph $G$ is called $k$-leaf-connected if $|V(G)|\geq k+1$ and given any subset $S\subseteq V(G)$ with $|S|=k,$ $G$ always has a spanning tree $T$ such that $S$ is precisely the set of leaves of $T.$ In this paper, we prove best possible sufficient conditions for a graph to be $k$-leaf-connected in terms of the first Zagreb index, second Zagreb index and hyper-Zagreb index of $G$ or its complement.
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