scholarly journals Randic type SDI energy of graph

2021 ◽  
Keyword(s):  
Energy Of Graph

scholarly journals The minimum covering signless laplacian energy of graph

2020 ◽  
Vol 1597 ◽  
pp. 012031
Author(s):  
Kavita Permi ◽  
H S Manasa ◽  
M C Geetha
Keyword(s):  
Laplacian Energy ◽  
Signless Laplacian ◽  
Energy Of Graph

scholarly journals Bounds on Energy and Laplacian Energy of Graphs

2017 ◽  
Vol 23 (2) ◽  
pp. 21-31
Author(s):  
Sridhara G ◽  
Rajesh Kanna
Keyword(s):  
Upper Bounds ◽  
Simple Graph ◽  
Laplacian Energy ◽  
Energy Of Graph ◽  
The Absolute

Let G be simple graph with n vertices and m edges. The energy E(G) of G, denotedby E(G), is dened to be the sum of the absolute values of the eigenvalues of G. Inthis paper, we present two new upper bounds for energy of a graph, one in terms ofm,n and another in terms of largest absolute eigenvalue and the smallest absoluteeigenvalue. The paper also contains upper bounds for Laplacian energy of graph.

scholarly journals The Energy Change of the Complete Multipartite Graph

2020 ◽  
Vol 36 (36) ◽  
pp. 309-317
Author(s):  
Haiying Shan ◽  
Changxiang He ◽  
Zhensheng Yu
Keyword(s):  
Linear Algebra ◽  
Singular Values ◽  
New Method ◽  
Energy Change ◽  
Natural Question ◽  
Complete Multipartite Graph ◽  
Multipartite Graph ◽  
Energy Of Graph ◽  
Complete Multipartite ◽  
Edge Addition

The energy of a graph is defined as the sum of the absolute values of all eigenvalues of the graph. Akbari et al. [S. Akbari, E. Ghorbani, and M. Oboudi. Edge addition, singular values, and energy of graphs and matrices. {\em Linear Algebra Appl.}, 430:2192--2199, 2009.] proved that for a complete multipartite graph $K_{t_1 ,\ldots,t_k}$, if $t_i\geq 2 \ (i=1,\ldots,k)$, then deleting any edge will increase the energy. A natural question is how the energy changes when $\min\{t_1 ,\ldots,t_k\}=1$. In this paper, a new method to study the energy of graph is explored. As an application of this new method, the above natural question is answered and it is completely determined how the energy of a complete multipartite graph changes when one edge is removed.

scholarly journals On the Seidel Energy of Certain Mesh Derived Networks

2019 ◽  
Vol 9 (2) ◽  
pp. 1905-1910
Keyword(s):  
Adjacency Matrix ◽  
Seidel Matrix ◽  
Energy Of Graph ◽  
The Absolute ◽  
Manual Calculation

The energy of graph G is defined as the sum of the absolute values of eigenvalues of the adjacency matrix A(G). The manual calculation of energy of graphs consumes several man hours. In this paper, we use MATLAB to generate the Seidel matrix and hence calculate the Seidel energy of some mesh derived networks.

scholarly journals Spectral Properties with the Difference between Topological Indices in Graphs

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Akbar Jahanbani ◽  
Roslan Hasni ◽  
Zhibin Du ◽  
Seyed Mahmoud Sheikholeslami
Keyword(s):  
Characteristic Polynomial ◽  
Lower Bounds ◽  
Adjacency Matrix ◽  
Spectral Properties ◽  
Main Tool ◽  
Topological Indices ◽  
Upper And Lower Bounds ◽  
New Energy ◽  
Energy Of Graph ◽  
The Difference

Let G be a graph of order n with vertices labeled as v1,v2,…,vn. Let di be the degree of the vertex vi, for i=1,2,…,n. The difference adjacency matrix of G is the square matrix of order n whose i,j entry is equal to di+dj−2−1/didj if the vertices vi and vj of G are adjacent or vivj∈EG and zero otherwise. Since this index is related to the degree of the vertices of the graph, our main tool will be an appropriate matrix, that is, a modification of the classical adjacency matrix involving the degrees of the vertices. In this paper, some properties of its characteristic polynomial are studied. We also investigate the difference energy of a graph. In addition, we establish some upper and lower bounds for this new energy of graph.

A note on the Laplacian resolvent energy of graphs

2019 ◽  
Vol 13 (06) ◽  
pp. 2050119
Author(s):  
M. Matejić ◽  
E. Zogić ◽  
E. Milovanović ◽  
I. Milovanović
Keyword(s):  
Lower Bounds ◽  
Connected Graph ◽  
Laplacian Eigenvalues ◽  
Energy Of Graph ◽  
Simple Connected Graph

Let [Formula: see text] be a simple connected graph with [Formula: see text] vertices, [Formula: see text] edges and let [Formula: see text] be its Laplacian eigenvalues. The Laplacian resolvent energy of graph [Formula: see text] is defined by [Formula: see text]. In this paper, we give some new lower bounds for the invariant [Formula: see text].

scholarly journals Минимальная доминирующая энергия Рандича графа

2017 ◽  
Author(s):  
P.S. Reddy ◽  
K.N. Prakasha ◽  
V.M. Siddalingaswamy
Keyword(s):  
Lower Bounds ◽  
Upper And Lower Bounds ◽  
Energy Of Graph

In this paper, we introduce the minimum dominating Randic energy of a graph and computed the minimum dominating Randic energy of graph. Also, obtained upper and lower bounds for the minimum dominating Randic energy of a graph.

scholarly journals The Energy of Cayley Graphs for Symmetric Groups of Order 24

2020 ◽  
pp. 1-6
Author(s):  
Amira Fadina Ahmad Fadzil ◽  
Nor Haniza Sarmin ◽  
Ahmad Erfanian
Keyword(s):  
Finite Group ◽  
Symmetric Group ◽  
Cayley Graph ◽  
Adjacency Matrix ◽  
Cayley Graphs ◽  
Symmetric Groups ◽  
Finite Graph ◽  
Energy Of Graph ◽  
A Finite Group

A Cayley graph of a finite group G with respect to a subset S of G is a graph where the vertices of the graph are the elements of the group and two distinct vertices x and y are adjacent to each other if xy−1 is in the subset S. The subset of the Cayley graph is inverse closed and does not include the identity of the group. For a simple finite graph, the energy of a graph can be determined by summing up the positive values of the eigenvalues of the adjacency matrix of the graph. In this paper, the graph being studied is the Cayley graph of symmetric group of order 24 where S is the subset of S4 of valency up to two. From the Cayley graphs, the eigenvalues are calculated by constructing the adjacency matrix of the graphs and by using some properties of special graphs. Finally, the energy of the respected Cayley graphs is computed and presented. Keywords: energy of graph; cayley graph; symmetric groups

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