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Degree kirchhoff index of unicyclic graphs

Webspecific graphs. Throughout this study, we used a graph to model the molecular structure, in which each edge denotes a chemical bond and each vertex expresses an atom between two atoms. 2. Exact Definition of Multiplicative Degree-Kirchhoff Index The multiplicative degree-Kirchhoff index of a connected graph is defined as the sum of the product ... WebOct 1, 2015 · This quantity is sometimes referred to as the “degree Kirchhoff index” (see , ) and the “additive degree-Kirchhoff index” (see , ). In [20] some properties of D R -index were presented and the unicyclic graphs with the minimum and the second minimum D R -value for unicyclic graphs were also completely characterized.

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WebOct 20, 2016 · First we consider the minimum Kirchhoff index of unicyclic graphs with perfect matching. Theorem 4.1. Among the graphs in U (2 m, m) with m ≥ 2, (i) for 2 ≤ m ≤ 4, C 2m is the unique graph with minimum Kirchhoff index, which is equal to 1 6 (4 m 3 − m); (ii) for m = 5, U(8, 2) is the unique graph with minimum Kirchhoff index, which is ... WebGeneral Randić Index of Unicyclic Graphs With Given Number of Pendant Vertices Tomáš Vetrík, Selvaraj Balachandran Pages: 83–88 DOI: 10.47443/dml.2024.0124. An Improved Lower Bound for the Degree Kirchhoff Index of Bipartite Graphs Ş. Burcu Bozkurt Altındağ, Igor Milovanović, Emina Milovanović, Marjan Matejić ... scam 1992 watch online movierulz https://traffic-sc.com

On the Kirchhoff index of a graph and the matchings of the …

WebMar 31, 2024 · The Kirchhoff index of a graph and the matchings of its subdivision. Recall that for a graph G of order n with Laplacian characteristic polynomial L ( G, x) = ∑ i = 0 n ( − 1) i c i x n − i, (1.2), (1.3) say τ ( G) = c n − 1 n; K f ( G) = c n − 2 τ ( G). So using the results about c i obtained in the previous section, the following ... Webextremal graph. Keywords. Kirchhoff index, Maximum degree, Unicyclic graphs 1 Introduction First we introduce some graph notations used in this paper. We only … WebAn electrical network is often modeled as a graph where every edge of the graph is assumed to be a resistor. The Kirchhoff index Kf(G) of a simple connected graph G is the sum of the resistances between every pair of vertices in G. In this paper, we determine the minimum Kirchhoff index among the unicyclic graphs with given girth and diameter. scam 1992 web series 720p download

The extremal Kirchhoff index of a class of unicyclic graphs 1

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Degree kirchhoff index of unicyclic graphs

On the Minimum Kirchhoff Index of Unicyclic Graphs …

WebNov 20, 2024 · Let G be a connected graph with vertex set V ( G) .The degree Kirchhoff index of G is defined as S ′ ( G) = ∑ { u, v } ⊆ V ( G) d ( u) d ( v) R ( u, v), where d ( u) is … WebOct 17, 2016 · Abstract. The Wiener index is the sum of distances between all pairs of distinct vertices in a connected graph, which is the oldest topological index related to molecular branching. In the article we characterize the graphs having the minimum Wiener index among all n -vertex unicyclic graphs with a fixed diameter.

Degree kirchhoff index of unicyclic graphs

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WebMar 14, 2024 · Many studies have been carried out to compute Kirchhoff indices for specific classes of graphs, to find bounds for the Kirchhoff indices of graphs, and to find the characteristic extremal graphs [4,5,6,7,8,9,10].Recently, a study has been made to explore the Kirchhoff index based on the degree of vertices regarding irregular … WebNov 29, 2024 · A dumbbell graph \(B_n(p,l,q)\) is a bicyclic graph of order n consisting of two vertex-disjoint cycle \(C_p\) and \(C_q\) with a path of length \(l-1\) jointing them. In this paper, explicit formulas of the (reverse) cover costs, the additive degree-Kirchhoff index (resp. multiplicative degree-Kirchhoff index) in terms of the effective resistance-based …

WebMar 7, 2024 · [4] Qinying Huang, Haiyan Chen, Qingying Deng, Resistance distances and the Kirchhoff index in double graphs. Journal of Applied Mathematics and Computing, 50(2016) 1-14. [5] Meiqiao Zhang, Xian’an Jin, Qingying Deng, The Minimal Coloring Number Of Any Non-splittable Z-colorable Link Is Four, Journal of Knot Theory and Its … WebFeb 26, 2015 · on the normalised laplacian spectrum, degree-kirchhoff index and spanning trees of graphs - volume 91 issue 3 Skip to main content Accessibility help We use cookies to distinguish you from other users and to provide you with a …

WebNov 20, 2024 · Let G be a connected graph with vertex set V ( G) .The degree Kirchhoff index of G is defined as S ′ ( G) = ∑ { u, v } ⊆ V ( G) d ( u) d ( v) R ( u, v), where d ( u) is the degree of vertex u, and R ( u, v) denotes the resistance distance between vertices u and v. In this paper, we characterize the graphs having maximum and minimum degree ... WebFeb 17, 2024 · Similarly, Chen and Zhang defined the multiplicative degree-Kirchhoff index of as . Moreover, the following relation between and was confirmed. Lemma 2 (See ). Let be a simple connected graph of order and size . Then, Nowadays, the (multiplicative degree-) Kirchhoff index has attracted a lot of attention from researchers over the few …

WebSep 20, 2024 · Sharp bounds for the second Zagreb index of unicyclic graphs. J Math Chem, 2007, 42(3): 565–574. Article MathSciNet Google Scholar Y Yang, X Jiang. Unicyclic graphs with extremal Kirchhoff index. MATCH Commun Math Comput Chem, 2008, 60(1): 107–120. MathSciNet MATH Google Scholar

WebSep 28, 2024 · According to Figures 5 and 6, it is clear that the multiplicative degree-Kirchhoff index of both the linear and circle graph is the fast growing, and the additive degree-Kirchhoff index is the second growing.Other than that, in the circle graph, whenever is odd or even, the Zagreb index is growing faster than Randic index and … sayings about greedy peopleWebJul 10, 2014 · Abstract. The resistance distance between two vertices of a connected graph is defined as the effective resistance between them in the corresponding electrical network constructed from by replacing each edge of with a unit resistor. The Kirchhoff index of is the sum of resistance distances between all pairs of vertices. In this paper, general … sayings about good peopleWebFor a graph, the SK index is equal to the half of the sum of the degrees of the vertices, the SK 1 index is equal to the half of the product of the degrees of the vertices, and the SK 2 index is equal to the half of the square of the sum of the degrees of the vertices. This paper shows a simple and unified approach to the greatest SK indices for unicyclic graphs by … sayings about grandchildrenhttp://mat76.mat.uni-miskolc.hu/~mnotes/downloader.php?article=mmn_781.pdf sayings about grace and mercyWebJun 1, 2016 · The Wiener index is the sum of distances between all pairs of distinct vertices in a connected graph, which is the oldest topological index related to molecular branching. In this article, we give a condition to determine the graphs having the smallest Wiener index among all unicyclic graphs given number of pendant vertices, and we also determine … scam 1992 web series all episodesWebFeb 28, 2024 · Abstract. There has been an upsurge of research on complex networks in recent years. The purpose of this paper is to study the mathematical properties of the random pentagonal chain networks with the help of graph theory. Based on the networks , we first obtain the expected value expressions of the Gutman index, Schultz index, … sayings about grandparents and grandchildrenWebJan 1, 2013 · The answer is provided in [4]: the minimal degree-Kirchhoff index among unicyclic graphs has a value of 2n 2 − 5 3 n − 5, so our lower bound does not miss this … sayings about grandparents love