指数型Sombor指标在完美匹配的单圈图中的极值问题

Extreme Value ofExponetial Sombor Index in Unicyclic Graph with Perfect Matching

摘要: Sombor指标是一种离散数学图论中的拓扑指标,能够清晰地反应图的特征。讨论拓扑指标的极值问题能够分析图的基本性质。本文讨论了在完美匹配的单圈图当中,指数型Sombor指标的极值问题。其中指数型Sombor指标定义为: e^SO(G) =_uv∈E(G)^{∑e√d2_G(u)+d2_G(v)} 本文的主要结论是: 若G∈U_2m,m，则 e^SO(G) ≤ e^SO(U_2m,m)且e^SO(U_2m,m) ≤ (m - 2)e^√5 + me√(m+1)²+4+e^2√2+e√(m+1)²+1等号成立当且仅当G≅U_2m,m,其中m为图G的匹配数。

Abstract: The Sombor Index is a Topological Index in Discrete Mathematical Graph Theory which can clearly reflect the characteristics of the graph. While the Extreme value of Topological Index is the key to analyse the basic properties of the graph. This paper discusses the Extreme Value of Exponential Sombor Index in Unicyclic Graph with Perfect Matching. The exponential Sombor index is defined as: e^SO(G) =_uv∈E(G)^{∑e√d2_G(u)+d2_G(v)} The main result of this paper is: If G∈U_2m,m, Then e^SO(G) ≤ e^SO(U_2m,m), e^SO(U_2m,m) ≤ (m - 2)e^√5 + me√(m+1)²+4+e^2√2+e√(m+1)²+1If and only if G≅U_2m,m the equal sign is established, Where m is the matching number of Graph G.