scholarly journals Energy of extended bipartite double graphs

2021 ◽  
Vol 87 (3) ◽  
pp. 653-660
Author(s):  
Harishchandra S. Ramane ◽  
◽  
B. Parvathalu ◽  
K. Ashoka
Keyword(s):  
Bipartite Graphs ◽  
Exact Relation ◽  
The Absolute ◽  
Graph Parameters

The energy of a graph is the sum of the absolute values of its eigenvalues. In this article, an exact relation between the energy of extended bipartite double graph and the energy of a graph together with some other graph parameters is given. As a consequence, equienergetic, borderenergetic, orderenergetic and non-hyperenergetic extended bipartite double graphs are presented. The obtained results generalize the existing results on equienergetic bipartite graphs.

scholarly journals On the Graceful Game

2020 ◽  
Vol 18 (3) ◽  
Author(s):  
Atilio Luiz ◽  
Simone Dantas ◽  
Luisa Ricardo
Keyword(s):  
Connected Graph ◽  
Bipartite Graphs ◽  
Absolute Difference ◽  
Complete Graphs ◽  
Graceful Labeling ◽  
Graph Games ◽  
First Results ◽  
Winning Strategies ◽  
Complete Bipartite Graphs ◽  
The Absolute

A graceful labeling of a graph G with m edges consists in labeling the vertices of G with distinct integers from 0 to m such that, when each edge is assigned the absolute difference of the labels of its endpoints, all induced edge labels are distinct. Rosa established two well known conjectures: all trees are graceful (1966) and all triangular cacti are graceful (1988). In order to contribute to both conjectures we study these problems in the context of graph games. The graceful game was introduced by Tuza in 2017 as a two-players game on a connected graph in which the players Alice and Bob take turns labeling the vertices with distinct integers from 0 to m. Alice’s goal is to gracefully label the graph as Bob’s goal is to prevent it from happening. In this work, we present the first results in this area by showing winning strategies for Alice and Bob in complete graphs, paths, cycles, complete bipartite graphs, caterpillars, prisms, wheels, helms, webs, gear graphs, hypercubes and some powers of paths.

scholarly journals Simple graph models of information spread in finite populations

2015 ◽  
Vol 2 (5) ◽  
pp. 150028 ◽  
Author(s):  
Burton Voorhees ◽  
Bergerud Ryder
Keyword(s):  
Information Diffusion ◽  
Transition Probability ◽  
Bipartite Graphs ◽  
Hitting Times ◽  
Antisymmetric Part ◽  
Directional Bias ◽  
Single Link ◽  
Fixation Probabilities ◽  
Circular Flows ◽  
Graph Parameters

We consider several classes of simple graphs as potential models for information diffusion in a structured population. These include biases cycles, dual circular flows, partial bipartite graphs and what we call ‘single-link’ graphs. In addition to fixation probabilities, we study structure parameters for these graphs, including eigenvalues of the Laplacian, conductances, communicability and expected hitting times. In several cases, values of these parameters are related, most strongly so for partial bipartite graphs. A measure of directional bias in cycles and circular flows arises from the non-zero eigenvalues of the antisymmetric part of the Laplacian and another measure is found for cycles as the value of the transition probability for which hitting times going in either direction of the cycle are equal. A generalization of circular flow graphs is used to illustrate the possibility of tuning edge weights to match pre-specified values for graph parameters; in particular, we show that generalizations of circular flows can be tuned to have fixation probabilities equal to the Moran probability for a complete graph by tuning vertex temperature profiles. Finally, single-link graphs are introduced as an example of a graph involving a bottleneck in the connection between two components and these are compared to the partial bipartite graphs.

Bounds and extremal graphs for Harary energy

2021 ◽  
pp. 2150149
Author(s):  
A. Alhevaz ◽  
M. Baghipur ◽  
H. A. Ganie ◽  
K. C. Das
Keyword(s):  
Connected Graph ◽  
Distance Matrix ◽  
Upper Bounds ◽  
Extremal Graphs ◽  
Lower And Upper Bounds ◽  
Energy Formula ◽  
Matrix Formula ◽  
The Absolute ◽  
Graph Parameters ◽  
Reciprocal Distance Matrix

Let [Formula: see text] be a connected graph of order [Formula: see text] and let [Formula: see text] be the reciprocal distance matrix (also called Harary matrix) of the graph [Formula: see text]. Let [Formula: see text] be the eigenvalues of the reciprocal distance matrix [Formula: see text] of the connected graph [Formula: see text] called the reciprocal distance eigenvalues of [Formula: see text]. The Harary energy [Formula: see text] of a connected graph [Formula: see text] is defined as sum of the absolute values of the reciprocal distance eigenvalues of [Formula: see text], that is, [Formula: see text] In this paper, we establish some new lower and upper bounds for [Formula: see text] in terms of different graph parameters associated with the structure of the graph [Formula: see text]. We characterize the extremal graphs attaining these bounds. We also obtain a relation between the Harary energy and the sum of [Formula: see text] largest adjacency eigenvalues of a connected graph.

scholarly journals On Color Energy of Few Classes of Bipartite Graphs and Corresponding Color Complements

1970 ◽  
Vol 8 (1) ◽  
pp. 7-14
Author(s):  
Prajakta Bharat Joshi ◽  
Mayamma Joseph
Keyword(s):  
Chromatic Number ◽  
Domination Number ◽  
Bipartite Graphs ◽  
Subject Classification ◽  
Proper Coloring ◽  
Colored Graph ◽  
Ams Subject Classification ◽  
Graph Parameters

For a given colored graph G, the color energy is defined as Ec(G) = Σλi, for i = 1, 2,…., n; where λi is a color eigenvalue of the color matrix of G, Ac (G) with entries as 1, if both the corresponding vertices are neighbors and have different colors; -1, if both the corresponding vertices are not neighbors and have same colors and 0, otherwise. In this article, we study color energy of graphs with proper coloring and L (h, k)-coloring. Further, we examine the relation between Ec(G) with the corresponding color complement of a given graph G and other graph parameters such as chromatic number and domination number. AMS Subject Classification: 05C15, 05C50

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

Bipartite Graphs and their Applications

1998 ◽  
Author(s):  
Armen S. Asratian ◽  
Tristan M. J. Denley ◽  
Roland Häggkvist
Keyword(s):  
Bipartite Graphs

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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