Results 161 to 170 of about 6,554 (178)
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2023
Summary: The PI index of a graph \(G\) is given by \(\operatorname{PI}(G)=\sum_{e\in E(G)} (|V(G)|-N_G(e))\), where \(N_G(e)\) is the number of equidistant vertices for the edge \(e\). Various topological indices of bicyclic graphs have already been calculated. In this paper, we obtained the exact value of the PI index of bicyclic graphs.
SC, Manju, K, Somasundaram
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Summary: The PI index of a graph \(G\) is given by \(\operatorname{PI}(G)=\sum_{e\in E(G)} (|V(G)|-N_G(e))\), where \(N_G(e)\) is the number of equidistant vertices for the edge \(e\). Various topological indices of bicyclic graphs have already been calculated. In this paper, we obtained the exact value of the PI index of bicyclic graphs.
SC, Manju, K, Somasundaram
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Extremal Bicyclic 3-Chromatic Graphs
Graphs and Combinatorics, 2014zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Tomescu, Ioan, Javed, Sana
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Bicyclic graphs with extremal cover cost
Applied Mathematics and Computation, 2021zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Lu, Jian, Pan, Xiang-Feng, Liu, Huiqing
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Reduced Sombor index of bicyclic graphs
Asian-European Journal of Mathematics, 2021The concept of Sombor indices (SO) of a graph was recently introduced by Gutman and the reduced Sombor index [Formula: see text] of a graph [Formula: see text] is defined by [Formula: see text] where [Formula: see text] is the degree of the vertex [Formula: see text].
Shiikhar Dorjsembe, Batmend Horoldagva
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On Bicyclic Graphs with Maximal Graovac-Ghorbani Index
Match Communications in Mathematical and in Computer Chemistry, 2023Graovac-Ghorbani index is a new version of the atom-bond connectivity index. D. Pacheco et al. [MATCH Commun. Math. Comput. Chem. 86 (2021) 429-448] conjectured a sharp lower and upper bounds to the Graovac-Ghorbani index for all bicyclic graphs. Motivated by their nice work, in this paper we determine the maximal Graovac-Ghorbani index of bicyclic ...
Song, Rui +3 more
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Minimal configuration bicyclic graphs
Linear and Multilinear Algebra, 2012The nullity η(G) of a graph G is the multiplicity of zero as an eigenvalue of the adjacency matrix of G. If η(G) = 1, then the core of G is the subgraph induced by the vertices associated with the nonzero entries of the kernel eigenvector. The set of vertices which are not in the core is the periphery of G.
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Bicyclic graphs with minimum energy
Linear and Multilinear Algebra, 2001If λ1, λ2,…,λn are the eigenvalues of a graph G, then the energy of this graph is denned as . For n⩾6, let be the graph obtained by joining n−5 pendant vertices to a vertex of degree three of the complete bipartite graph K 2. We show that for all values of n⩾6, S 4,4 n has the minimal energy among all n vertex connected bicyclic graphs with at most one
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On bicyclic graphs with minimal energies
Journal of Mathematical Chemistry, 2005zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zhang, Jianbin, Zhou, Bo
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Unbalanced unicyclic and bicyclic graphs with extremal spectral radius
Czechoslovak Mathematical Journal, 2020zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Belardo F., Brunetti M., Ciampella A.
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Degree Kirchhoff Index of Bicyclic Graphs
Canadian Mathematical Bulletin, 2017AbstractLet G be a connected graph with vertex set V(G).The degree Kirchhoò index of G is defined as S'(G) = Σ{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 Kirchhoò index among all n ...
Zikai Tang, Hanyuan Deng
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