Results 91 to 100 of about 580,793 (206)

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
openaire   +2 more sources

Certain Aspects of Spectra of Unicyclic Graphs [PDF]

, 2006
Supervisor: Bhaba Kr. SarmaThis thesis aims at filling some conspicuous gaps in the study of spectra of unicyclic graphs, and answering some recent questions on relations between the structure of a unicyclic graph and the spectrum of its adjacency matrix.
Nath, Milan
core   +1 more source

Optimal resistor networks

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

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, Klavžar Sandi, Lehner Florian, Soltani Samaneh   +3 more
doaj   +1 more source

Unicyclic graphs with maximal energy [PDF]

, 2002
Let G be a graph on n vertices and let λ1,λ2,…,λn be its eigenvalues. The energy of G is defined as E(G)=|λ1|+|λ2|+⋯+|λn|. For various classes of unicyclic graphs, the graphs with maximal energy are determined.
Woo, Ching-Wah, Hou, Yaoping, Gutman, Ivan   +2 more
core   +1 more source

Zonal Labeling of Graphs

Indonesian Journal of Combinatorics
A planar graph is said to be zonal when is possible to label its vertices with the nonzero elements of ℤ3, in such a way that the sum of the labels of the vertices on the boundary of each zone is 0 in ℤ3.
Christian Barrientos, Sarah Minion
doaj   +1 more source

Eigenspaces for \(-2\) in signed line graphs

The American Journal of Combinatorics
It is known that \(-2\) appears in the spectrum of a connected signed line graph if and only if its root is either (a) a balanced signed graph, not a tree, that spans a switching of the complete signed graph or (b) an unbalanced simply signed graph ...
Zoran Stanić
doaj   +1 more source

Zagreb Indices of Trees, Unicyclic and Bicyclic Graphs With Given (Total) Domination

IEEE Access, 2019
Let G = (V, E) be a (molecular) graph. For a family of graphs G, the first Zagreb index M1 and the second Zagreb index M2 have already studied. In particular, it has been presented, the first Zagreb index M1 and the second Zagreb index M2 of trees T in ...
Doost Ali Mojdeh, Mohammad Habibi, Leila Badakhshian, Yongsheng Rao   +3 more
doaj   +1 more source

Greedoids on Vertex Sets of Unicycle Graphs

CoRR, 2009
9 pages; 4 ...
Vadim E. Levit, Eugen Mandrescu
openaire   +3 more sources

Subtrees and independent subsets in unicyclic graphs and unicyclic graphs with fixed segment sequence

, 2020
In the study of topological indices two negative correlations are well known: that between the number of subtrees and the Wiener index (sum of distances), and that between the Merrifield-Simmons index (number of independent vertex subsets) and the Hosoya index (number of independent edge subsets).
Andriantiana, Eric Ould Dadah, Wang, Hua
openaire   +2 more sources