Results 91 to 100 of about 412,655 (203)
The Harary Index of All Unicyclic Graphs with Given Diameter
Discrete Dynamics in Nature and Society, 2018 The Harary index of G is the sum of reciprocals of distance between any two vertices in G. In this paper, we obtain the graphs with the maximum and second-maximum Harary indices among n-vertex unicyclic graphs with diameter d.
Bao-Hua Xing +3 more
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Maximum Laplacian energy of unicyclic graphs
Discrete Applied Mathematics, 2017 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Kinkar Chandra Das +3 more
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Journal of Mathematics, Volume 2025, Issue 1, 2025.The multiplicative sum Zagreb index of a graph G is defined as the product of the sum of the degrees of adjacent vertices of G. A molecular tree is an acyclic connected graph with maximum degree at most 4. A vertex in a molecular tree with degree 3 or 4 is referred to as a branching vertex. In this paper, we consider the class of all molecular trees of
Sadia Noureen +6 more
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On the eccentric connectivity index of unicyclic graphs
, 2018 Summary: In this paper, we obtain the upper and lower bounds on the eccentricity connectivity index of unicyclic graphs with perfect matchings. Also, we give some lower bounds on the eccentric connectivity index of unicyclic graphs with given matching numbers.
Nacaroglu, Yasar, Maden, Ayse Dilek
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On the nullity and the matching number of unicyclic graphs [PDF]
, 2009 Let G be a graph with n vertices and ν(G) be the matching number of G. Let η(G) denote the nullity of G (the multiplicity of the eigenvalue zero of G). It is well known that if G is a tree, then η(G)=n-2ν(G). Tan and Liu [X. Tan, B.
Yan, Weigen +2 more
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On the Maximum SC Index of Chemical Unicyclic Graphs
Journal of Mathematics, Volume 2025, Issue 1, 2025.The sum‐connectivity (SC) index of a graph G is defined as SCG=∑μν∈EG1/Θμ+Θν, where Θμ denotes the vertex degree of μ in G. In this paper, the fourth largest value of SC index for the chemical unicyclic graphs of order n ≥ 7 is determined.
Hui-Yan Cheng +3 more
wiley +1 more source
Graphs which have pancyclic complements
International Journal of Mathematics and Mathematical Sciences, 1978 Let p and q denote the number of vertices and edges of a graph G, respectively. Let Δ(G) denote the maximum degree of G, and G¯ the complement of G. A graph G of order p is said to be pancyclic if G contains a cycle of each length n, 3≤n≤p.
H. Joseph Straight
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Mathematika, Volume 70, Issue 4, October 2024.Abstract Given a graph on n$n$ vertices with m$m$ edges, each of unit resistance, how small can the average resistance between pairs of vertices be? There are two very plausible extremal constructions — graphs like a star, and graphs which are close to regular — with the transition between them occurring when the average degree is 3.
J. Robert Johnson, Mark Walters
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Some Results on the Signless Laplacian Spectra of Unicyclic Graphs [PDF]
, 2011 We determine the second to fourth largest (resp. the second smallest) signless Laplacian spectral radii and the second to fourth largest signless Laplacian spreads together with the corresponding graphs in the class of unicyclic graphs with n vertices ...
Muhuo Liu
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