• Kyungpook Mathematical Journal
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• v.58 no.2
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• pp.221-229
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• 2018

The first Zagreb eccentricity index $E_1(G)$ of a graph G is defined as the sum of squares of the eccentricities of the vertices. In this paper some bounds for the first Zagreb eccentricity index and first Zagreb degree eccentricity index are computed.

• Journal of applied mathematics & informatics
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• v.33 no.3_4
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• pp.365-377
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• 2015

For a (molecular) graph, the first and second Zagreb indices (M₁ and M₂) are two well-known topological indices, first introduced in 1972 by Gutman and Trinajstić. The first Zagreb index M₁ is equal to the sum of the squares of the degrees of the vertices, and the second Zagreb index M₂ is equal to the sum of the products of the degrees of pairs of adjacent vertices. Let $K_{n_1,n_2}^{P}$ with n₁ $\leq$ n₂, n₁ + n₂ = n and p < n₁ be the set of bipartite graphs obtained by deleting p edges from complete bipartite graph K_n1,n2. In this paper, we determine sharp upper and lower bounds on Zagreb indices of graphs from $K_{n_1,n_2}^{P}$ and characterize the corresponding extremal graphs at which the upper and lower bounds on Zagreb indices are attained. As a corollary, we determine the extremal graph from $K_{n_1,n_2}^{P}$ with respect to Zagreb coindices. Moreover a problem has been proposed on the first and second Zagreb indices.

• Pediatric Gastroenterology, Hepatology & Nutrition
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• v.21 no.3
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• pp.214-217
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• 2018

Inflammatory bowel disease (IBD) is a well-recognized risk factor for thrombotic events in adults but data on children are scarce. In the great majority of adult patients, thrombotic events are usually deep vein thrombosis and pulmonary embolism. Other sites such as jugular veins are extremely rare. We present a case of Lemierre syndrome in an adolescent girl with active ulcerative colitis and discuss possible risk factors. This is the first reported case of severe Lemierre syndrome with thrombus extension to cranial veins in a patient with ulcerative colitis. Early recognition of Lemierre syndrome in patients who present with rapidly worsening symptoms of neck pain, fever and signs of pharyngitis is imperative because it increases a chance of favorable prognosis. It is important for pediatricians treating IBD patients not to underestimate possible thrombotic events in children with IBD. Recognition of additional risk factors is crucial for prompt diagnosis and adequate treatment.

• Journal of applied mathematics & informatics
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• v.39 no.3_4
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• pp.339-358
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• 2021

Zagreb indices and their modified versions of a molecular graph are important descriptors which can be used to characterize the structural properties of organic molecules from different aspects. In this work, we investigate some properties of the modified second multiplicative Zagreb index of graphs with given connectivity. In particular, we obtain the maximum values of the modified second multiplicative Zagreb index with fixed number of cut edges, or cut vertices, or edge connectivity, or vertex connectivity of graphs. Furthermore, we characterize the corresponding extremal graphs.

• Journal of applied mathematics & informatics
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• v.34 no.3_4
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• pp.319-330
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• 2016

The hyper-Zagreb index HM(G) of a simple graph G is defined as the sum of the terms (d_u+d_v)² over all edges uv of G, where d_u denotes the degree of the vertex u of G. In this paper, we present several upper and lower bounds on the hyper-Zagreb index in terms of some molecular structural parameters and relate this index to various well-known molecular descriptors.

• Journal of applied mathematics & informatics
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• v.29 no.1_2
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• pp.327-335
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• 2011

Explicit formulas are given for the first and second Zagreb index, degree-distance and Wiener-type invariants of splice and link of graphs. As a consequence, the first and second Zagreb coindex of these classes of composite graphs are also computed.

• Korean Journal of Mathematics
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• v.23 no.3
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• pp.401-408
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• 2015

The first and second Zagreb indices of a graph G are defined as $M_1(G)={\sum}_{{\nu}{\in}V}d_G({\nu})^2$ and $M_2(G)={\sum}_{u{\nu}{\in}E(G)}d_G(u)d_G({\nu})$. where $d_G({\nu})$ is the degree of the vertex ${\nu}$. G is called a k-apex tree if k is the smallest integer for which there exists a subset X of V (G) such that ${\mid}X{\mid}$ = k and G-X is a tree. In this paper, we determine the maximum Zagreb indices in the class of all k-apex trees of order n and characterize the corresponding extremal graphs.

• Pediatric Gastroenterology, Hepatology & Nutrition
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• v.24 no.3
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• pp.256-264
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• 2021

Purpose: Data on the relationship between gastroesophageal reflux (GER) and brief resolved unexplained events (BRUE) in infants is scarce. The aim of this study was to identify the characteristics of combined multichannel intraluminal impedance-pH (MII-pH) monitoring in infants who have experienced BRUE. Methods: We conducted a prospective study of infants who were hospitalized on account of BRUE and required 24-hour MII-pH monitoring. Results: Twenty-one infants (mean age, 4.7 months; range, 0.9-8.9 months; male/female, 11/10) participated in this study. BRUE symptoms associated with GER were found in 10 infants (47.6%). Based on the RI on pH-metry alone, only 7 (33.3%) infants were diagnosed with GERD. More than 100 GER episodes detected by MII were found in 10 (47.6%) infants. Nineteen percent of infants were diagnosed with GERD based on both pH and MII. Conclusion: Both acid and non-acid reflux seem to play a significant role in the pathogenesis of GER-related BRUE in infants.

• The korean journal of orthodontics
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• v.42 no.5
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• pp.263-269
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• 2012

Objective: To evaluate the antimicrobial effect of different frequencies of brushing with fluoride toothpaste on the levels of salivary mutans streptococci and lactobacilli in children undergoing fixed orthodontic treatment. Methods: The study included 22 patients scheduled for fixed orthodontic therapy distributed between 2 groups with different hygiene regimes. All the subjects received identical braces, bands, and brackets bonded with the same material. Stimulated saliva samples were obtained before placement of the appliance and at 6, 12, and 18 weeks during the therapy. Saliva samples were cultured on selective microbial agar for the detection of microorganisms. Results: Salivary mutans streptococci were significantly suppressed throughout the experimental period in the group that brushed 4 times a day as compared to the group that brushed twice a day. Salivary lactobacilli were not significantly affected by the frequency of brushing with 0.32% sodium fluoride (NaF) toothpaste. Conclusions: The use of 0.32% NaF-containing toothpaste more than 3 times a day has effective antimicrobial activity on mutans streptococci but not lactobacilli in the saliva of children with fixed orthodontic appliances.

• Coupled systems mechanics
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• v.7 no.6
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• pp.755-774
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• 2018

The Ritz method is known as very successful strategy for discretizing continuous problems, but it has never been used for solving systems of algebraic equations. The Iterated Ritz Method (IRM) is a novel iterative solver based on the discretized Ritz procedure applied at each iteration step. With an appropriate choice of coordinate vectors, the method may be efficient in linear, nonlinear and optimization problems. Additionally, some iterative methods can be explained as special cases of this approach, which helps to understand advantages and limitations of these methods and gives motivation for their improvement in sense of IRM. In this paper, some ideas for generation of efficient coordinate vectors are presented. The algorithm was developed and tested independently and then implemented into the open source program FEAP. Method has been successfully applied to displacement based (even ill-conditioned) models of structural engineering practice. With this original approach, a new iterative solution strategy has been opened.