On the inverse sum indeg energy of trees

2021 ◽  
Author(s):  
H. Hatefi ◽  
H. Abdollahzadeh Ahangar ◽  
R. Khoeilar ◽  
S. M. Sheikholeslami
Keyword(s):  
Text Entry ◽  
The Absolute ◽  
Square Matrix

Let [Formula: see text] be a graph of order [Formula: see text] and [Formula: see text] be the degree of the vertex [Formula: see text], for [Formula: see text]. The [Formula: see text] matrix of [Formula: see text] is the square matrix of order [Formula: see text] whose [Formula: see text]-entry is equal to [Formula: see text] if [Formula: see text] is adjacent to [Formula: see text], and zero otherwise. Let [Formula: see text], be the eigenvalues of [Formula: see text] matrix. The [Formula: see text] energy of a graph [Formula: see text], denoted by [Formula: see text], is defined as the sum of the absolute values of the eigenvalues of [Formula: see text] matrix. In this paper, we prove that the star has the minimum [Formula: see text] energy among trees.

On the Randić Matrix and Randić Energy

2021 ◽  
pp. 2150155
Author(s):  
H. Hatefi ◽  
H. Abdollahzadeh Ahangar ◽  
R. Khoeilar ◽  
S. M. Sheikholeslami
Keyword(s):  
Text Entry ◽  
The Absolute ◽  
Square Matrix

Let [Formula: see text] be a graph with [Formula: see text] vertices, and let [Formula: see text] be the degree of the vertex [Formula: see text] in the graph [Formula: see text]. The Randić matrix of [Formula: see text] is the square matrix of order [Formula: see text] whose [Formula: see text]-entry is equal to [Formula: see text] if the vertex [Formula: see text] and the vertex [Formula: see text] of [Formula: see text] are adjacent, and [Formula: see text] otherwise. The Randić eigenvalues of [Formula: see text] are the eigenvalues of its Randić matrix and the Randić energy of [Formula: see text] is the sum of the absolute values of its Randić eigenvalues. In this paper, we obtain some new results for the Randić eigenvalues and the Randić energy of a graph.

scholarly journals Seidel Equienergetic Graphs

2016 ◽  
Vol 16 ◽  
pp. 62-69
Author(s):  
Harishchandra S. Ramane ◽  
Mahadevappa M. Gundloor ◽  
Sunilkumar M. Hosamani
Keyword(s):  
Characteristic Polynomial ◽  
Regular Graphs ◽  
Seidel Matrix ◽  
The Absolute ◽  
Equienergetic Graphs ◽  
Square Matrix

The Seidel matrix S(G) of a graph G is the square matrix with diagonal entries zeroes and off diagonal entries are – 1 or 1 corresponding to the adjacency and non-adjacency. The Seidel energy SE(G) of G is defined as the sum of the absolute values of the eigenvalues of S(G). Two graphs G1 and G2 are said to be Seidel equienergetic if SE(G1) = SE(G2). We establish an expression for the characteristic polynomial of the Seidel matrix and for the Seidel energy of the join of regular graphs. Thereby construct Seidel non cospectral, Seidel equienergetic graphs on n vertices, for all n ≥ 12

scholarly journals New Results on Zagreb Energy of Graphs

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Seyed Mahmoud Sheikholeslami ◽  
Akbar Jahanbani ◽  
Rana Khoeilar
Keyword(s):  
Vertex Set ◽  
The Absolute ◽  
Equienergetic Graphs ◽  
Square Matrix

Let G be a graph with vertex set V G = v 1 , … , v n , and let d i be the degree of v i . The Zagreb matrix of G is the square matrix of order n whose i , j -entry is equal to d i + d j if the vertices v i and v j are adjacent, and zero otherwise. The Zagreb energy ZE G of G is the sum of the absolute values of the eigenvalues of the Zagreb matrix. In this paper, we determine some classes of Zagreb hyperenergetic, Zagreb borderenergetic, and Zagreb equienergetic graphs.

scholarly journals Degree Subtraction Adjacency Polynomial and Energy of Graphs obtained from Complete Graph

2020 ◽  
pp. 263-277
Author(s):  
Harishchandra S. Ramane ◽  
Hemaraddi N. Maraddi ◽  
Daneshwari Patil ◽  
Kavita Bhajantri
Keyword(s):  
Characteristic Polynomial ◽  
Complete Graph ◽  
Adjacency Matrix ◽  
Degree Of A Vertex ◽  
The Absolute ◽  
Square Matrix

The degree subtraction adjacency matrix of a graph G is a square matrix DSA(G)=[dij], in which dij=d(vi)-d(vj), if the vertices vi and vj are adjacent and dij=0, otherwise, where d(u) is the degree of a vertex u. The DSA energy of a graph is the sum of the absolute values of the eigenvalues of DSA matrix. In this paper, we obtain the characteristic polynomial of the DSA matrix of graphs obtained from the complete graph. Further we study the DSA energy of these graphs.

Bulk standards for low-temperature biological x-ray microanalysis

1984 ◽  
Vol 42 ◽  
pp. 282-283
Author(s):  
P. Echlin ◽  
M. McKoon ◽  
E.S. Taylor ◽  
C.E. Thomas ◽  
K.L. Maloney ◽  
...  
Keyword(s):  
Phase Separation ◽  
Low Temperature ◽  
Analytical Method ◽  
Salt Solutions ◽  
Absolute Concentration ◽  
Cooling Process ◽  
X Ray ◽  
The Absolute ◽  
Analytical Procedures ◽  
Electrical Conductors

Although sections of frozen salt solutions have been used as standards for x-ray microanalysis, such solutions are less useful when analysed in the bulk form. They are poor thermal and electrical conductors and severe phase separation occurs during the cooling process. Following a suggestion by Whitecross et al we have made up a series of salt solutions containing a small amount of graphite to improve the sample conductivity. In addition, we have incorporated a polymer to ensure the formation of microcrystalline ice and a consequent homogenity of salt dispersion within the frozen matrix. The mixtures have been used to standardize the analytical procedures applied to frozen hydrated bulk specimens based on the peak/background analytical method and to measure the absolute concentration of elements in developing roots.

A Quantitative Ultrastructural Study of Peripheral Blood Lymphocytes Containing Parallel Tubular Arrays in Epstein-Barr Virus and Cytomegalo-Virus Mononucleosis

1981 ◽  
Vol 39 ◽  
pp. 454-455
Author(s):  
C. M. Payne ◽  
P. M. Tennican
Keyword(s):  
Peripheral Blood ◽  
Lymphocyte Count ◽  
Epstein Barr Virus ◽  
Absolute Lymphocyte Count ◽  
Peripheral Blood Lymphocytes ◽  
Clinical State ◽  
Barr Virus ◽  
The Absolute ◽  
Epstein Barr ◽  
Tubular Arrays

In the normal peripheral circulation there exists a sub-population of lymphocytes which is ultrastructurally distinct. This lymphocyte is identified under the electron microscope by the presence of cytoplasmic microtubular-like inclusions called parallel tubular arrays (PTA) (Figure 1), and contains Fc-receptors for cytophilic antibody. In this study, lymphocytes containing PTA (PTA-lymphocytes) were quantitated from serial peripheral blood specimens obtained from two patients with Epstein -Barr Virus mononucleosis and two patients with cytomegalovirus mononucleosis. This data was then correlated with the clinical state of the patient.It was determined that both the percentage and absolute number of PTA- lymphocytes was highest during the acute phase of the illness. In follow-up specimens, three of the four patients' absolute lymphocyte count fell to within normal limits before the absolute PTA-lymphocyte count.In one patient who was followed for almost a year, the absolute PTA- lymphocyte count was consistently elevated (Figure 2). The estimation of absolute PTA-lymphocyte counts was determined to be valid after a morphometric analysis of the cellular areas occupied by PTA during the acute and convalescent phases of the disease revealed no statistical differences.

Polarity Determination in Sphalerite and Wurtzite Structures

1990 ◽  
Vol 48 (2) ◽  
pp. 500-501
Author(s):  
Stuart McKernan ◽  
C. Barry Carter
Keyword(s):  
Opposite Polarity ◽  
Single Domain ◽  
Polar Material ◽  
Electron Microscopic ◽  
Dynamical Interaction ◽  
X Ray ◽  
Polarity Determination ◽  
The Absolute ◽  
Microscopic Techniques

The determination of the absolute polarity of a polar material is often crucial to the understanding of the defects which occur in such materials. Several methods exist by which this determination may be performed. In bulk, single-domain specimens, macroscopic techniques may be used, such as the different etching behavior, using the appropriate etchant, of surfaces with opposite polarity. X-ray measurements under conditions where Friedel’s law (which means that the intensity of reflections from planes of opposite polarity are indistinguishable) breaks down can also be used to determine the absolute polarity of bulk, single-domain specimens. On the microscopic scale, and particularly where antiphase boundaries (APBs), which separate regions of opposite polarity exist, electron microscopic techniques must be employed. Two techniques are commonly practised; the first [1], involves the dynamical interaction of hoLz lines which interfere constructively or destructively with the zero order reflection, depending on the crystal polarity. The crystal polarity can therefore be directly deduced from the relative intensity of these interactions.

516: A Simplified Method to Estimate the Absolute Renal Uptake of 99MTC-DMSA: Evaluation with a New Model using the Radioactivity of Nephrectomy Specimens as Reference

2005 ◽  
Vol 173 (4S) ◽  
pp. 140-141
Author(s):  
Mariana Lima ◽  
Celso D. Ramos ◽  
Sérgio Q. Brunetto ◽  
Marcelo Lopes de Lima ◽  
Carla R.M. Sansana ◽  
...  
Keyword(s):  
New Model ◽  
Renal Uptake ◽  
Simplified Method ◽  
The Absolute

Translocation Relative to Range

Methodology ◽  
2008 ◽  
Vol 4 (3) ◽  
pp. 132-138 ◽  
Author(s):  
Michael Höfler
Keyword(s):  
Risk Difference ◽  
Binary Outcomes ◽  
Number Needed To Treat ◽  
Likert Scales ◽  
Psychological Science ◽  
The Absolute ◽  
The Difference ◽  
Variance Parameters ◽  
Standardized Index ◽  
Maximum Possible Magnitude

A standardized index for effect intensity, the translocation relative to range (TRR), is discussed. TRR is defined as the difference between the expectations of an outcome under two conditions (the absolute increment) divided by the maximum possible amount for that difference. TRR measures the shift caused by a factor relative to the maximum possible magnitude of that shift. For binary outcomes, TRR simply equals the risk difference, also known as the inverse number needed to treat. TRR ranges from –1 to 1 but is – unlike a correlation coefficient – a measure for effect intensity, because it does not rely on variance parameters in a certain population as do effect size measures (e.g., correlations, Cohen’s d). However, the use of TRR is restricted on outcomes with fixed and meaningful endpoints given, for instance, for meaningful psychological questionnaires or Likert scales. The use of TRR vs. Cohen’s d is illustrated with three examples from Psychological Science 2006 (issues 5 through 8). It is argued that, whenever TRR applies, it should complement Cohen’s d to avoid the problems related to the latter. In any case, the absolute increment should complement d.

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