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The Extremal Unicyclic Graphs With Given Girth for Exponential VDB Topological Indices

Journal of Mathematics
Topological indices are widely used molecular structure descriptors in chemistry and pharmaceutics, which help analyze and predict the physicochemical properties and biological activity of compounds.
Zhenhua Su, Zikai Tang
doaj   +3 more sources

On the Core of a Unicyclic Graph [PDF]

Ars Mathematica Contemporanea, 2011
A set S is independent in a graph G if no two vertices from S are adjacent. By core(G) we mean the intersection of all maximum independent sets. The independence number alpha(G) is the cardinality of a maximum independent set, while mu(G) is the size of ...
Levit, Vadim E., Mandrescu, Eugen
core   +5 more sources

Locating Eigenvalues of a Symmetric Matrix whose Graph is Unicyclic

Trends in Computational and Applied Mathematics, 2021
We present a linear-time algorithm that computes in a given real interval the number of eigenvalues of any symmetric matrix whose underlying graph is unicyclic.
R. O. Braga, V. M. Rodrigues, R. O. Silva   +2 more
doaj   +2 more sources

On the least signless Laplacian eigenvalue of a non-bipartite connected graph with fixed maximum degree [PDF]

Journal of Inequalities and Applications, 2017
In this paper, we determine the unique graph whose least signless Laplacian eigenvalue attains the minimum among all non-bipartite unicyclic graphs of order n with maximum degree Δ and among all non-bipartite connected graphs of order n with maximum ...
Shu-Guang Guo, Rong Zhang
doaj   +2 more sources

On the maximum atom-bond sum-connectivity index of unicyclic graphs with given diameter

AIMS Mathematics
Let $ G = (V(G), E(G)) $ be a simple connected graph with vertex set $ V(G) $ and edge set $ E(G) $. The atom-bond sum-connectivity (ABS) index was proposed recently and is defined as $ ABS(G) = \sum_{uv\in E(G)}\sqrt{\frac{d_{G}(u)+d_{G}(v)-2}{d_{G}(u ...
Zhen Wang, Kai Zhou
doaj   +2 more sources

Resolving an Open Problem on the Exponential Arithmetic–Geometric Index of Unicyclic Graphs

Mathematics
Recently, the exponential arithmetic–geometric index (EAG) was introduced. The exponential arithmetic–geometric index (EAG) of a graph G is defined as EAG(G)=∑vivj∈E(G)edi+dj2didj, where di represents the degree of the vertex vi in G.
Kinkar Chandra Das, Jayanta Bera
doaj   +2 more sources

The inverse of the incidence matrix of a unicyclic graph [PDF]

Linear and multilinear algebra, 2022
The vertex-edge incidence matrix of a (connected) unicyclic graph G is a square matrix which is invertible if and only if the cycle of G is an odd cycle.
Ryan Hessert, Sudipta Mallik
semanticscholar   +1 more source

On Irregular Colorings of Unicyclic Graph Family

CAUCHY, 2023
Irregular coloring is a proper coloring and each vertex on a graph must have a different code. The color code of a vertex v is  where  and    is the number of vertices that are adjacent to v and colored i.
A. I. Kristiana, D. Dafik, Q. A’yun, R. Adawiyah, R. Alfarisi   +4 more
semanticscholar   +1 more source

Incidence and Laplacian matrices of wheel graphs and their inverses

The American Journal of Combinatorics, 2023
It has been an open problem to find the Moore-Penrose inverses of the incidence, Laplacian, and signless Laplacian matrices of families of graphs except trees and unicyclic graphs.
Jerad Ipsen, Sudipta Mallik
doaj   +1 more source

The k-Metric Dimension of a Unicyclic Graph

Mathematics, 2021
Given a connected graph G=(V(G),E(G)), a set S⊆V(G) is said to be a k-metric generator for G if any pair of different vertices in V(G) is distinguished by at least k elements of S.
A. Estrada-Moreno
semanticscholar   +1 more source