Some Relations Between Rank, Vertex Cover Number and Energy of Graph

IF 2.9 2区 化学 Q2 CHEMISTRY, MULTIDISCIPLINARY Match-Communications in Mathematical and in Computer Chemistry Pub Date : 2023-01-01 DOI:10.46793/match.89-3.653a
S. Akbari, Hamideh Alizadeh, M. Fakharan, M. Habibi, Samane Rabizadeh, Soheyr Rouhani
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Abstract

In this paper, we extend some results of [F. Shaveisi, lower bounds on the vertex cover number and energy of graphs, MATCH Commun. Math. Comput. Chem, 87(3) (2022) 683-692] which state some relations between the vertex cover and other parameters, such as the order and maximum or minimum degree of graphs. Also, we prove that for a graph G, E(G) ≥ 2β(G)−2Ce(G) and so E(G) ≥ 2β(G) − 2C(G), where E(G), β(G), Ce(G) and C(G) denote the energy, vertex cover, number of even cycles and number of cycles in G, respectively. For these both inequalities we investigate their equality. Finally, we give some relations between E(G),γ(G) and γt(G), where γ(G) and γt(G) are domination number and total domination number of G, respectively.
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图的秩、顶点覆盖数与能量的关系
本文推广了[F]的一些结果。Shaveisi,图的顶点覆盖数和能量的下界,MATCH common。数学。第一版。化学,87(3)(2022)683-692],其中陈述了顶点覆盖与其他参数之间的一些关系,例如图的顺序和最大或最小度。同时证明了对于图G, E(G)≥2β(G) - 2Ce(G),因此E(G)≥2β(G) - 2C(G),其中E(G)、β(G)、Ce(G)和C(G)分别表示G中的能量、顶点覆盖、偶环数和环数。对于这两个不等式,我们考察了它们的相等性。最后给出了E(G)、γ(G)和γt(G)之间的关系,其中γ(G)和γt(G)分别是G的支配数和总支配数。
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来源期刊
CiteScore
4.40
自引率
26.90%
发文量
71
审稿时长
2 months
期刊介绍: MATCH Communications in Mathematical and in Computer Chemistry publishes papers of original research as well as reviews on chemically important mathematical results and non-routine applications of mathematical techniques to chemical problems. A paper acceptable for publication must contain non-trivial mathematics or communicate non-routine computer-based procedures AND have a clear connection to chemistry. Papers are published without any processing or publication charge.
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