Results 91 to 100 of about 828 (207)
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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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
wiley +1 more source
On the nullity of the line graph of unicyclic graph with depth one
, 2012 A connected graph with a unique cycle is called a unicyclic graph. A unicyclic graph with depth one may be thought of as being obtained from a cycle by appending ni pendent edges on each vertex vi in the cycle Ct (for some integer t⩾3), denoted by Cn1,n2,
Fan, Yi-Zheng, Li, Hong-Hai, Su, Li
core +1 more source
Complement of the generalized total graph of fields
AKCE International Journal of Graphs and Combinatorics, 2020 Let R be a commutative ring and H be a multiplicative prime subset of R. The generalized total graph is the undirected simple graph with vertex set R and two distinct vertices x and y are adjacent if For a field F, is the only multiplicative prime subset
T. Tamizh Chelvam, M. Balamurugan
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Greedoids on Vertex Sets of Unicycle Graphs
CoRR, 2009 9 pages; 4 ...
Vadim E. Levit, Eugen Mandrescu
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The Least Algebraic Connectivity of Graphs
Discrete Dynamics in Nature and Society, 2015 The algebraic connectivity of a graph is defined as the second smallest eigenvalue of the Laplacian matrix of the graph, which is a parameter to measure how well a graph is connected.
Guisheng Jiang, Guidong Yu, Jinde Cao
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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
On the core of a unicyclic graph
, 2011 A set S ⊆ V is independent in a graph G = (V,E) if no two vertices from S are adjacent. By core(G) we mean the intersection of all maximum independent sets.
Vadim E. Levit, Eugen Mandrescu
core
Trees with Distinguishing Index Equal Distinguishing Number Plus One
Discussiones Mathematicae Graph Theory, 2020 The distinguishing number (index) D(G) (D′ (G)) of a graph G is the least integer d such that G has an vertex (edge) labeling with d labels that is preserved only by the trivial automorphism.
Alikhani Saeid +3 more
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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
wiley +1 more source