Results 1 to 10 of about 963 (204)

Further Results on the Resistance-Harary Index of Unicyclic Graphs

Mathematics, 2019
The Resistance-Harary index of a connected graph G is defined as R H ( G ) = ∑ { u , v } ⊆ V ( G ) 1 r ( u , v ) , where r ( u , v ) is the resistance distance between vertices u and v in G.
Shu-Bo Chen, Jia-Bao Liu, Xiang-Feng Pan   +2 more
exaly   +4 more sources

Unicyclic Graphs with the Fourth Extremal Wiener Indices

Journal of Chemistry, 2020
A graph is called unicyclic if the graph contains exactly one cycle. Unicyclic graphs with the fourth extremal Wiener indices are characterized. It is shown that, among all unicyclic graphs with n≥8 vertices, C5Sn−4 and C2u1,u2S3,Sn−4 attain the fourth ...
Guangfu Wang, Yujun Yang, Yuliang Cao, Shoujun Xu   +3 more
doaj   +2 more sources

New Diagonal Graph Ramsey Numbers of Unicyclic Graphs

Theory and Applications of Graphs, 2023
Grossman conjectured that R(G, G) = 2 · |V (G)| − 1, for all simple connected unicyclic graphs G of odd girth and |V (G)| ≥ 4. In this note, we prove his conjecture for various classes of G containing a triangle.
Richard M. Low, Ardak Kapbasov
doaj   +3 more sources

On Variable Sum Exdeg Indices of Quasi-Tree Graphs and Unicyclic Graphs

Discrete Dynamics in Nature and Society, 2020
In this work, by using the properties of the variable sum exdeg indices and analyzing the structure of the quasi-tree graphs and unicyclic graphs, the minimum and maximum variable sum exdeg indices of quasi-tree graphs and quasi-tree graphs with perfect ...
Xiaoling Sun, Jianwei Du
doaj   +2 more sources

Regularity of the edge ideals of perfect [ν,h]-ary trees and some unicyclic graphs [PDF]

Heliyon
We compute the Castelnuovo-Mumford regularity of the quotient rings of edge ideals of perfect [ν,h]-ary trees and some unicyclic graphs.
Fatima Tul Zahra, Muhammad Ishaq, Sarah Aljohani   +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

Lower bounds on trees and unicyclic graphs with respect to the misbalance rodeg index [PDF]

Heliyon
The Misbalance Rodeg (MR) index stands out among the 148 discrete Adriatic indices demonstrating considerable predictive capabilities in evaluations carried out by the International Academy of Mathematical Chemistry.
Nasrin Dehgardi, Mahdieh Azari, Yilun Shang   +2 more
doaj   +2 more sources

Extremal Permanents of Laplacian Matrices of Unicyclic Graphs

Axioms
The extremal problem of Laplacian permanents of graphs is a classical and challenging topic in algebraic combinatorics, where the inherent #P-complete complexity of permanent computation renders this pursuit particularly intractable.
Tingzeng Wu, Xiuhong Wang, Xiangshuai Dong   +2 more
doaj   +2 more sources

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

Unicyclic graphs with bicyclic inverses [PDF]

, 2017
summary:A graph is nonsingular if its adjacency matrix $A(G)$ is nonsingular. The inverse of a nonsingular graph $G$ is a graph whose adjacency matrix is similar to $A(G)^{-1}$ via a particular type of similarity.
Panda, Swarup Kumar
core   +2 more sources