Lower bounds of graph energy in terms of matching number

2018 ◽  
Vol 549 ◽  
pp. 276-286 ◽  
Author(s):  
Dein Wong ◽  
Xinlei Wang ◽  
Rui Chu
Keyword(s):  
Lower Bounds ◽  
Matching Number ◽  
Graph Energy

scholarly journals The Minimum Edge Covering Energy of a Graph

2021 ◽  
Vol 45 (6) ◽  
pp. 969-975
Author(s):  
SAMIRA SABETI ◽  
◽  
AKRAM BANIHASHEMI DEHKORDI ◽  
SAEED MOHAMMADIAN SEMNANI
Keyword(s):  
Lower Bounds ◽  
Upper And Lower Bounds ◽  
Underlying Graph ◽  
Graph Energy ◽  
Edge Covering

In this paper, we introduce a new kind of graph energy, the minimum edge covering energy, ECE(G). It depends both on the underlying graph G, and on its particular minimum edge covering CE. Upper and lower bounds for ECE(G) are established. The minimum edge covering energy and some of the coefficients of the polynomial of well-known families of graphs like Star, Path and Cycle Graphs are computed

A note on the relationship between graph energy and determinant of adjacency matrix

2019 ◽  
Vol 11 (01) ◽  
pp. 1950001
Author(s):  
Igor Ž. Milovanović ◽  
Emina I. Milovanović ◽  
Marjan M. Matejić ◽  
Akbar Ali
Keyword(s):  
Lower Bounds ◽  
Adjacency Matrix ◽  
Bipartite Graphs ◽  
Simple Graph ◽  
Graph Invariants ◽  
Graph Energy ◽  
The Matrix ◽  
Matrix Formula ◽  
The Relationship

Let [Formula: see text] be a simple graph of order [Formula: see text], without isolated vertices. Denote by [Formula: see text] the adjacency matrix of [Formula: see text]. Eigenvalues of the matrix [Formula: see text], [Formula: see text], form the spectrum of the graph [Formula: see text]. An important spectrum-based invariant is the graph energy, defined as [Formula: see text]. The determinant of the matrix [Formula: see text] can be calculated as [Formula: see text]. Recently, Altindag and Bozkurt [Lower bounds for the energy of (bipartite) graphs, MATCH Commun. Math. Comput. Chem. 77 (2017) 9–14] improved some well-known bounds on the graph energy. In this paper, several inequalities involving the graph invariants [Formula: see text] and [Formula: see text] are derived. Consequently, all the bounds established in the aforementioned paper are improved.

scholarly journals Tight lower bounds on the matching number in a graph with given maximum degree

2018 ◽  
Vol 89 (2) ◽  
pp. 115-149 ◽  
Author(s):  
Michael A. Henning ◽  
Anders Yeo
Keyword(s):  
Lower Bounds ◽  
Maximum Degree ◽  
Matching Number

Interval Packing and Covering in the Boolean Lattice

1996 ◽  
Vol 5 (4) ◽  
pp. 373-384 ◽  
Author(s):  
Konrad Engel
Keyword(s):  
Lower Bounds ◽  
Pairwise Disjoint ◽  
Boolean Lattice ◽  
Covering Number ◽  
Matching Number ◽  
Packing And Covering ◽  
Minimum Number ◽  
Fractional Numbers

Let be the hypergraph whose points are the subsets X of [n] := {1,…,n} with l≤ |X| ≤ u, l < u, and whose edges are intervals in the Boolean lattice of the form I = {C ⊆[n] : X⊆C⊆Y} where |X| = l, |Y| = u, X ⊆ Y.We study the matching number i.e. the the maximum number of pairwise disjoint edges, and the covering number i.e. the minimum number of points which cover all edges. We prove that max and that for every ε > 0 the inequalities hold, where for the lower bounds we suppose that n is not too small. The corresponding fractional numbers can be determined exactly. Moreover, we show by construction that

scholarly journals On Lower Bounds for the Matching Number of Subcubic Graphs

2016 ◽  
Vol 85 (2) ◽  
pp. 336-348 ◽  
Author(s):  
P. E. Haxell ◽  
A. D. Scott
Keyword(s):  
Lower Bounds ◽  
Matching Number ◽  
Subcubic Graphs

Lower Bounds on the Uniquely Restricted Matching Number

2019 ◽  
Vol 35 (1) ◽  
pp. 353-361 ◽  
Author(s):  
M. Fürst ◽  
D. Rautenbach
Keyword(s):  
Lower Bounds ◽  
Matching Number

The minimum vertex–vertex dominating Laplacian energy of a graph

2021 ◽  
Author(s):  
N. V. Sayinath Udupa ◽  
R. S. Bhat
Keyword(s):  
Lower Bounds ◽  
Dominating Set ◽  
Domination Number ◽  
Upper And Lower Bounds ◽  
Underlying Graph ◽  
Laplacian Energy ◽  
Graph Energy ◽  
Number Formula

Let [Formula: see text] denote the set of all blocks of a graph [Formula: see text]. Two vertices are said to vv-dominate each other if they are vertices of the same block. A set [Formula: see text] is said to be vertex–vertex dominating set (vv-dominating set) if every vertex in [Formula: see text] is vv-dominated by some vertex in [Formula: see text]. The vv-domination number [Formula: see text] is the cardinality of the minimum vv-dominating set of [Formula: see text]. In this paper, we introduce new kind of graph energy, the minimum vv-dominating Laplacian energy of a graph denoting it as LE[Formula: see text]. It depends both on the underlying graph of [Formula: see text] and the particular minimum vv-dominating set of [Formula: see text]. Upper and lower bounds for LE[Formula: see text] are established and we also obtain the minimum vv-dominating Laplacian energy of some family of graphs.

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