<abstract xmlns="http://www.w3.org/1999/xhtml">

In this article the concept of domination in signed graphs is examined from an alternate perspective and a new definition of the same is introduced. A vertex subset D of a signed graph S is a dominating set, if for each vertex v not in D there exists a vertex u ∈ D such that the sign of the edge uv is positive. The domination number γ (S) of S is the minimum cardinality among all the dominating sets of S. We obtain certain bounds of γ (S) and present a necessary and su cient condition for a dominating set to be a minimal dominating set. Further, we characterise the signed graphs having small and large values for domination number.
</abstract>

On domination in signed graphs

<abstract xmlns="http://www.w3.org/1999/xhtml">

In this paper, we report on PIN-code typing behaviour on touchscreen devices of 112 subjects. Detailed statistical analysis revealed that the major di erence between subjects is in inter-key latency. Key-press duration variations are insignificant compared to inter-key latency variations. Subjects were grouped into meaningful clusters using clustering. The resulting clusters were of slow, medium, and fast typists. The dataset was split randomly into two equal size subsets. The first subset was used to train different synthetic data generators, while the second subset was used to evaluate an authentication attack using the generated synthetic data. The evaluation showed that slow typists were the hardest to attack. Both the dataset and the software are publicly available at <ext-link ext-link-type="uri" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://github.com/margitantal68/sapipin_paper">https://github.com/margitantal68/sapipin_paper</ext-link>.
</abstract>

Sapientia Hungarian University of Transylvania

SapiPin: Observations on PIN-code typing dynamics

<abstract xmlns="http://www.w3.org/1999/xhtml">

In an isolate-free graph 𝒵 = (V𝒵, E𝒵), a set <italic>C</italic> of vertices is termed as a connected certified dominating set of 𝒵 if, |N𝒵(<italic>u</italic>) ∩ (V𝒵\<italic>C</italic>)| = 0 or |N𝒵(<italic>u</italic>) ∩ (V𝒵\<italic>C</italic>)| ≥ 2 ∀u ∈<italic>C</italic>, and the subgraph 𝒵[<italic>C</italic>] induced by <italic>C</italic> is connected. The cardinality of the minimal connected certified dominating set of graph 𝒵 is called the connected certified domination number of 𝒵 denoted by γcerc (<italic>Z</italic>). In graph 𝒵, if the deletion of any arbitrary edge changes the connected certified domination number, then we call it a connected certified domination edge critical. If the deletion of any random edge does not a ect the connected certified domination number, then we refer to it as a connected certified domination edge stable graph. In this paper, we investigate those graphs which are connected certified domination edge critical and stable upon edge removal. We then study some properties of connected certified domination edge critical and stable graphs.
</abstract>

Connected certified domination edge critical and stable graphs

<abstract xmlns="http://www.w3.org/1999/xhtml">

Let G be a connected graph with n vertices, m edges. The distance signless Laplacian matrix DQ(G) is defined as DQ(G) = Diag(Tr(G)) + D(G), where Diag(Tr(G)) is the diagonal matrix of vertex transmissions and D(G) is the distance matrix of G. The distance signless Laplacian eigenvalues of G are the eigenvalues of DQ(G) and are denoted by δ1Q(G), δ2Q(G), ..., δnQ(G). δ1Q is called the distance signless Laplacian spectral radius of DQ(G). In this paper, we obtain upper and lower bounds for SDQ (G) in terms of the Wiener index, the transmission degree and the order of the graph.
</abstract>

On the spread of the distance signless Laplacian matrix of a graph

<abstract xmlns="http://www.w3.org/1999/xhtml">

The energy E(G) of a graph G is the sum of the absolute values of eigenvalues of G and the Seidel energy ES(G) is the sum of the absolute values of eigenvalues of the Seidel matrix S of G. In this paper, some relations between the energy and Seidel energy of a graph in terms of different graph parameters are presented. Also, the inertia relations between the graph eigenvalue and Seidel eigenvalue of a graph are given. The results in this paper generalize some of the existing results.
</abstract>

Karnatak University’s, Karnatak Arts College

Some relations between energy and Seidel energy of a graph

<abstract xmlns="http://www.w3.org/1999/xhtml">

Automatic detection of tissue types on whole-slide images (WSI) is an important task in computational histopathology that can be solved with convolutional neural networks (CNN) with high accuracy. However, the black-box nature of CNNs rightfully raises concerns about using them for this task. In this paper, we reformulate the task of tissue type detection to multiple binary classification problems to simplify the justification of model decisions. We propose an adapted Bag-of-local-Features interpretable CNN for solving this problem, which we train on eight newly introduced binary tissue classification datasets. The performance of the model is evaluated simultaneously with its decision-making process using logit heatmaps. Our model achieves better performance than its non-interpretable counterparts, while also being able to provide human-readable justification for decisions. Furthermore, the problem of data scarcity in computational histopathology is accounted for by using data augmentation techniques to improve both the performance and even the validity of model decisions. The source code and binary datasets can be accessed at: <ext-link ext-link-type="uri" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://github.com/galigergergo/BolFTissueDetect">https://github.com/galigergergo/BolFTissueDetect</ext-link>.
</abstract>

Explainable patch-level histopathology tissue type detection with bag-of-local-features models and data augmentation

<abstract xmlns="http://www.w3.org/1999/xhtml">

E-super arithmetic graceful labelling of a graph G is a bijection f from the union of the vertex set and edge set to the set of positive integers (1, 2, 3, … |V(G) ∪ E(G)|) such that the edges have the labels from the set {1, 2, 3, …, |E(G)|} and the induced mapping f* given by f* (uv) = f(u) + f(v) − f(uv) for uv ∈ E(G) has the range {|V(G) ∪ E(G)| + 1, |V(G) ∪ E(G)| + 2, …, |V(G)| + 2|E(G)|}
In this paper we prove that Hi(m, m) and Hi(1) (m, m) and chain of even cycles C4,n, C6,n are E-super arithmetic graceful.
</abstract>

E-super arithmetic graceful labelling of Hi(m, m), Hi(1) (m, m) and chain of even cycles

<abstract xmlns="http://www.w3.org/1999/xhtml">

Text mining is an intriguing area of research, considering there is an abundance of text across the Internet and in social medias. Nevertheless outliers pose a challenge for textual data processing. The ability to identify this sort of irrelevant input is consequently crucial in developing high-performance models. In this paper, a novel unsupervised method for identifying outliers in text data is proposed. In order to spot outliers, we concentrate on the degree of similarity between any two documents and the density of related documents that might support integrated clustering throughout processing. To compare the e ectiveness of our proposed approach with alternative classification techniques, we performed a number of experiments on a real dataset. Experimental findings demonstrate that the suggested model can obtain accuracy greater than 98% and performs better than the other existing algorithms.
</abstract>

Textual outlier detection with an unsupervised method using text similarity and density peak

<abstract xmlns="http://www.w3.org/1999/xhtml">

Let G be a connected graph with vertex set V(G)and edge set E(G). The eccentric connectivity index of G is defined as <inline-formula>
<alternatives>
<inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_ausi-2023-0009_eq_001.png"></inline-graphic>
<math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><munder><mo>∑</mo><mrow><mi>ν</mi><mo>∈</mo><mtext>V</mtext><mrow><mo>(</mo><mtext>G</mtext><mo>)</mo></mrow></mrow></munder><mrow><mtext>ec</mtext><mrow><mo>(</mo><mi>ν</mi><mo>)</mo></mrow><mtext> </mtext><mtext>deg</mtext><mrow><mo>(</mo><mi>ν</mi><mo>)</mo></mrow></mrow></mrow></math>
<tex-math>\sum\limits_{\nu\in{\rm{V}}\left({\rm{G}}\right)}{{\rm{ec}}\left(\nu\right)\,{\rm{deg}}\left(\nu\right)}</tex-math>
</alternatives>
</inline-formula> where ec(v) the eccentricity of a vertex v and deg(v)is its degree and denoted by ɛc(G). In this paper, we investigate the eccentric connectivity index of the transformation graph Gxy+.
</abstract>

Faculty of Sciences, Department of Mathematics

Eccentric connectivity index in transformation graph Gxy+

<abstract xmlns="http://www.w3.org/1999/xhtml">

The rupture degree is one the most important vulnerability parameter in networks which are modelled by graphs. Let <italic>G</italic>(<italic>V</italic> (<italic>G</italic>),<italic>E</italic> (<italic>G</italic>)) be a simple undirected graph. The rupture degree is defined by <italic>r</italic>(<italic>G</italic>) = max<italic>{w</italic>(<italic>G</italic>–<italic>S</italic> )–<italic>|S |</italic>–<italic>m</italic>(<italic>G</italic>–<italic>S</italic> ):<italic>S ⊂ V</italic> (<italic>G</italic>) and <italic>w</italic>(<italic>G</italic>–<italic>S</italic> )>1<italic>}</italic> where m(<italic>G</italic>–<italic>S</italic> ) is the order of a largest connected component in <italic>G</italic>–<italic>S</italic> and <italic>w</italic>(<italic>G</italic>–<italic>S</italic> ) is the number of components of <italic>G</italic>–<italic>S</italic>, respectively. In this paper, we consider the vertex contraction method based on the network agglomeration operation for each vertex of <italic>G</italic>. Then, we have presented two graph vulnerability parameters called by <italic>agglomeration rupture degree</italic> and <italic>average lower agglomeration rupture degree</italic>. Furthermore, the exact values of them for some graph families are given. Finally, we proposed a polynomial time heuristic algorithm to obtain the values of <italic>agglomeration rupture degree</italic> and <italic>average</italic>
</abstract>

Pamukkale University, Faculty of Engineering

On agglomeration-based rupture degree in networks and a heuristic algorithm

<abstract xmlns="http://www.w3.org/1999/xhtml">

Interstitial Lung Diseases (ILDs) represent a heterogeneous group of several rare diseases that are di cult to predict, diagnose and monitor. There are no predictive biomarkers for ILDs, clinical signs are similar to the ones for other lung diseases, the radiological features are not easy to recognize, and require manual radiologist review. Data-driven support for ILD prediction, diagnosis and disease-course monitoring are great unmet need. Numerous image processing techniques and computer-aided diagnostic and decision-making support methods have been developed over the recent years. The current review focuses on such solutions, discussing advancements on the fields of Quantitative CT, Complex Networks, and Convolutional Neural Networks.
</abstract>

University Research, Innovation and Service Center, Óbuda University

Enhanced imagistic methodologies augmenting radiological image processing in interstitial lung diseases

<abstract xmlns="http://www.w3.org/1999/xhtml">

A graph G is said to be a semi-splitting block graph if there exists a graph H such that SB(H) ≌ G. This paper establishes a characterisation of semi-splitting block graphs based on the partition of the vertex set of G. The vertex (edge) connectivity and p-connectedness (p-edge connectedness) of SB(G) are examined. For all integers a, b with 1 &lt; a &lt; b, the existence of the graph G for which κ (G) = a, κ (SB(G)) = b and λ (G) = a, λ (SB(G)) = b are proved independently. The characterization of graphs with κ(SB(G)) = κ (G) and a necessary condition for graphs with κ (SB(G)) = λ (SB(G)) are achieved.
</abstract>

On connectivity of the semi-splitting block graph of a graph

AHEAD OF PRINT

Volume 15 (2023): Issue 2 (December 2023)

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