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刘海琴.三个圈图的两类冠图的ABC指数[J].南华大学学报(自然科学版),2019,33(5):64~67.[LIU Haiqin.The Atom-Bond Connectivity Index of Two Kinds of Corona Graphs of Three Cycle Graphs[J].Journal of University of South China(Science and Technology),2019,33(5):64~67.]

三个圈图的两类冠图的ABC指数

The Atom-Bond Connectivity Index of Two Kinds of Corona Graphs of Three Cycle Graphs

投稿时间：2019-06-03

DOI：

中文关键词: 冠图剖分点—边冠图 ABC指数

英文关键词:corona graph the subdivision vertex-edge corona graph ABC index

基金项目:山西农业大学科技创新基金项目(2014010);山西省青年科技研究基金项目(201801D221013)

作者	单位	E-mail
刘海琴	山西农业大学文理学院,山西太谷 030801	3525327764@qq.com

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中文摘要:

图G和H两者的点冠图,记作GH,定义为使图G的每一顶点分别与图H的一个拷贝的所有顶点相连。类似地,三个图的冠图记作G₁G₂G₃,定义为(G₁G₂)G₃,三个图G₁,G₂,G₃的剖分点—边冠图记为GS₁(GV₂GE₃)。图的ABC指数定义为:ABC(G)=∑uv∈E(G)d(u)+d(v)-2d(u)d(v),其中E(G)表示图G的边集,d(u),d(v)分别表示对应边的两顶点u,v的度。主要研究了三个圈图的这两类冠图的ABC指数。

英文摘要:

The corona graph of G and H,recorded as GH,defined as joining every vertex of G to each vertex of one copy of H.Analogously,the corona graph of three graphs denoted as G₁G₂G₃,defined as (G₁G₂)G₃.The subdivision vertex-edge corona graph of G₁ with G₂ and G₃,denoted by GS₁(GV₂GE₃).A novel atom-bond connectivity index for a (molecular) graph is defined as ∑uv∈E(G)d(u)+d(v)-2d(u)d(v),where E(G) is the edge set of G,d(u),d(v) are the vertex degree of u,v,respectively.In this paper,the atom-bond connectivity index of two kinds of corona graphs of three cycle graphs have been calculated.

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