Degree kirchhoff index of unicyclic graphs
WebApr 1, 2024 · 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 ... WebNov 10, 2024 · Similar to the Wiener index, the Kirchhoff index of a graph is defined as. This invariant has wide applications in electric circuit, physical interpretations, chemistry, and graph theory [12–16]. In 2012, Gutman et al. introduced the concept of the degree resistance distance defined as. Palacios called it as additive degree-Kirchhoff index in .
Degree kirchhoff index of unicyclic graphs
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WebAbstract For a connected graph G, the Kirchhoff index is defined as K f ( G ) = ∑ 1 ≤ i < j ≤ n R G ( v i , v j ) and the multiplicative eccentricity resistance-distance index ξ R ∗ ( G ) = ∑ { v i... 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 ...
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. http://mat76.mat.uni-miskolc.hu/~mnotes/downloader.php?article=mmn_781.pdf
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. WebFeb 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, …
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 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 … rullstol panthera s3WebFeb 17, 2024 · Similarly, Chen and Zhang defined the multiplicative degree-Kirchhoff index of as . Moreover, the following relation between and was confirmed. Lemma 2 … scary face dogWebThe 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 ,a nd R(u, v) denotes the resistance distance between … scary face easy drawWebwhere M 1 (Γ) and F (Γ) present the first Zagreb and forgotten indices of the (molecular) graph, respectively. Furthermore, they found the bounds of the Lz index for acyclic graphs. Dehgardi and Liu in 2024 extended these results of the Lz index for acyclic graphs under the condition of maximum degree [].Zeng and Wu (2024) determined the sharp upper … scary face clownWebOct 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 ... rullstol panthera u3WebThe Kirchhoff index is also much studied in the literature. Extremal unicyclic graphs with respect to the Kirchhoff index were determined in [15,27,28]. Deng also studied the Kirchhoff index of fully loaded unicyclic graphs [15] and graphs with many cut edges [8]. Zhou [30] characterized the extremal graphs with given matching rullbyealWebSep 30, 2024 · The degree Kirchhoff index of G is defined as K f ... In this paper, we determine maximum degree Kirchhoff index of n-vertex unicyclic graphs with fixed … rull wand