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A 2-edge-connected graph G is minimally 2-edge-connected if deleting arbitrary edge of G always leaves a graph which is not 2-edge-connected. In this paper, we completely characterize the (minimally) 2-edge-connected graphs with given size having the maximal signless Laplacian (Laplacian) index. [ABSTRACT FROM AUTHOR]

In this paper, we study the signless Laplacian spectral Turán type problem in terms of the size, obtain sharp upper bounds on the signless spectral radius of C 3 ( C 4 )-free graphs with given size and minimum degree δ ≥ 2 , and characterize the corresponding extremal graphs completely. [ABSTRACT FROM AUTHOR]

A c-cyclic graph is a connected graph with n vertices and n + c−1 edges. In this paper, we consider the problem that: in the class of graphs, each of which is the complement graph of a c-cyclic graph with n vertices, which graph has the largest A α -spectral radius. We shall show that, for 0 ≤ c ≤ n − 4 , the extremal graph must be a graph with an isolated vertex. This implies that the maximum degree of G is larger, then the A α -spectral radius of its complement graph is also larger. We also determine the structure of the extremal graph with largest A α -spectral radius among the class of graphs, each of which is the complement graph of a c-cyclic graph with n vertices and maximum degree n−1 for 0 ≤ c ≤ n − 3 and n−2 for 0 ≤ c ≤ n − 4 , respectively. [ABSTRACT FROM AUTHOR]

Let G be a simple undirected graph. For real number α ∈ [0, 1], Nikiforov defined the Aα-matrix of G as Aα(G) = αD(G) + (1 − α)A(G), where A(G) and D(G) are the adjacency matrix and the degree diagonal matrix of G respectively. In this paper, we obtain a sharp upper bound on the largest eigenvalue ρα(G) of Aα(G) for α ∈ [1/2, 1). Employing this upper bound, we prove that 'For connected G1 and G2 with n vertices and m edges, if the maximum degree Δ(G1) ≥ 2α(1 − α)(2m − n + 1) + 2α and Δ(G1) > Δ(G2), then ρ α (G 1) > ρ α (G 2) '. Let λα(G) denote the least eigenvalue of Aα(G). For α ∈ (1/2, 1), we prove that 'For two connected G1 and G2, if the minimum degree δ (G 1) ≤ 1 1 − α − 2 and δ(G1) < δ(G2), then λα(G1) < λα(G2)'. [ABSTRACT FROM AUTHOR]

Let g (G) denote the girth of a graph G. In this paper, we determine the unique graph with the maximum least Q-eigenvalue among all unicyclic graphs of order n = 6k (k ≥ 8) with perfect matchings. For the cases when n = 6k + 2 and n = 6k + 4, we prove that g (G) = 3 if G is a graph with the maximum least Q-eigenvalue, and provide a conjecture and a problem on the sharp upper bound of the least Q-eigenvalue. [ABSTRACT FROM AUTHOR]

Let G be a simple undirected graph. For any real number α ∈ [ 0 , 1 ] , Nikiforov defined the A α -matrix of G as A α (G) = α D (G) + (1 - α) A (G) , where A(G) and D(G) are the adjacency matrix and the degree diagonal matrix of G respectively. The largest eigenvalue of A α (G) is called the A α -spectral radius of G. In this paper, we give sharp upper bounds on the A α -spectral radius of C 4 -free graphs and Halin graphs for α ∈ [ 1 / 2 , 1) respectively. [ABSTRACT FROM AUTHOR]

In this paper, we study the algebraic connectivity of a Hamiltonian graph, and determine all Hamiltonian graphs whose algebraic connectivity attain the minimum among all Hamiltonian graphs onnvertices. [ABSTRACT FROM AUTHOR]

TheQ-indexof graphGis the largest eigenvalueq(G)of its signless Laplacian. In this paper, we prove that the graphhas the maximalQ-index among all outer-planar graphs of ordern. [ABSTRACT FROM PUBLISHER]

Abstract: A rational cuboid is a rectangular parallelepiped whose edges and face diagonals all have rational lengths. In this paper, we consider the problem: are there rational cuboids with a given face? In a sense, we reduce the problem to a finite calculation. [Copyright &y& Elsevier]

Abstract Denote by L g, l the lollipop graph obtained by attaching a pendant path P = v g v g + 1 ⋯ v g + l (l ≥ 1) to a cycle C = v 1 v 2 ⋯ v g v 1 (g ≥ 3). A F g , l − g r a p h of order n ≥ g + 1 is defined to be the graph obtained by attaching n − g − l pendent vertices to some of the nonpendant vertices of L g, l in which each vertex other than v g + l − 1 is attached at most one pendant vertex. A F g , l ∘ -graph is a F g , l − g r a p h in which v g is attached with pendant vertex. Denote by q min the least Q − e i g e n v a l u e of a graph. In this paper, we proceed on considering the domination number, the least Q -eigenvalue of a graph as well as their relation. Further results obtained are as follows: (i) some results about the changing of the domination number under the structural perturbation of a graph are represented; (ii) among all nonbipartite unicyclic graphs of order n , with both domination number γ and girth g (g ≤ n − 1), the minimum q min attains at a F g , l -graph for some l ; (iii) among the nonbipartite graphs of order n and with given domination number which contain a F g , l ∘ -graph as a subgraph, some lower bounds for q min are represented; (iv) among the nonbipartite graphs of order n and with given domination number n 2. [ABSTRACT FROM AUTHOR]

Objective: The aim of this study was to assess the therapeutic effects and complications of tension band wiring (TBW) through the use of double-cannulated screws versus conventional TBW in the treatment of olecranon fractures., Methods: Eligible participants were randomly assigned to 2 groups to undergo different methods of fixation. The related indices and data of the 2 groups were collected for comparative analysis after an average follow-up of 32.7±6.6 months., Results: Average fracture healing time was 11.4 weeks in the double-screw TBW group and 12.6±1.8 weeks in the conventional TBW group (p=0.000). There was significant difference in complications related to fixation between the 2 groups. In the double-screw TBW group (42 patients), 2 patients felt screw head prominence with no pain and requested no further intervention; in contrast, 21 patients experienced complications associated with internal fixation in the conventional TBW group. Mean Mayo Elbow Performance Score (MEPS) score was 87.90±6.0 in the double-screw TBW group, compared to 83.67±6.6 in the conventional TBW group at 24-month follow-up (p=0.002). The rate of elbow function in the double-screw TBW group (29/42, 69.05%) was higher than that of the conventional TBW group (16/46, 34.78%) (p=0.000)., Conclusion: In comparison with conventional TBW, TBW with double-cannulated screws can significantly reduce complications, lower reoperation rate, improve elbow function, shorten healing time, as well as diminish surgical trauma.

Objective: To explore the risk factors of deep vein thrombosis (DVT) in lower extremities., Methods: Retrospective data analyses were performed for a total of 1264 DVT patients at our department from January 2010 to December 2012., Results: Among them, 984 cases (77.85%) were over 40 years old, no overt cause was found for 642 cases (50.79%), 142 cases (11.23%) had a clear history of trauma before onset (without surgery). Among 316 recurrent postoperative cases, there were the surgical histories of orthopedics (n = 142, 11.23%), gynecology (n = 90, 7.12%), general practice (n = 42, 3.32%), vascular (n = 23, 1.82%), urological (n = 12, 0.94%) and others (n = 7, 0.55%). Ten cases (0.79%) occurred after suffering bedridden chronic diseases. And 20 cases (1.58%) were caused by conditions during pregnancy or postpartum period.had Malignant tumors were found in 25 (1.98%) patients. After long-term uses of hormones, 10 patients (0.79%) of rheumatoid arthritis had a recurrence.Owing to varicose veins, 27 patients (2.14%) recurred. Eight patients (0.63%) had a history of drug abuse, 2 cases (0.16%) suffered depression and 62 cases (4.9%) were recurrent., Conclusion: There are many causative factors of DVT so that prevention is of great importance. We should pay more attention to the prevention and treatment of high-risk DVT patients.

Objective: To explore the clinical efficacies of endovascular therapy for traumatic arterial intima injury, arterial pseudoaneurysm and arteriovenous fistula., Methods: From October 2009 to December 2011, 24 patients of arterial intima injury, arterial pseudoaneurysm and arteriovenous fistula underwent endovascular therapy including embolism and stent implantation, etc., Results: Among them, 14 patients were punctured directly and another 10 were punctured after the exposure of arteries. The interventions included embolism (n = 3), embolism plus covered stent implantation (n = 2), covered stent implantation (n = 12) and bare stent implantation (n = 7). And the surgical success rate was 100%. After endoluminal treatment, arterial blood flow recovered, arterial pseudoaneurysm shrank, local pain relieved and venous blood pressure decreased., Conclusion: As an effective therapy for traumatic arterial intima injury, arterial pseudoaneurysm and arteriovenous fistula, endovascular therapy has minimal trauma, fewer complications and satisfactory outcomes.

Objective: To summarize the clinical experiences of treating deep venous thrombosis (DVT) with retrievable vena cava filter., Methods: A total of 180 patients with DVT in unilateral lower extremity were recruited. There were 82 males and 98 females with an average age of 46 years old. After the diagnosis of vascular color Doppler ultrasound, retrievable vena cava filter was implanted through contralateral femoral vein. Simultaneously another 114 patients underwent femoral vein embolectomy. All cases received the post-operative therapies of anticoagulation, thrombolysis and vasodilation., Results: The implantation of retrievable vena cava filter was successful in all cases. Among 142 cases of attempted extraction, 116 filters were extracted successfully at Days 12 - 24. The success rate was 81.69%. Filters captured thrombosis in 34 cases (29.31%)., Conclusion: As a safe and efficacious method, the implantation of retrievable vena cava filter prevents the occurrence of pulmonary embolism in the patients with DVT in unilateral lower extremity. Its timely extraction may avoid the long-term complications.

Objective: To explore the effects of surgical procedure combined with the intravascular minimal invasive technique for the treatment of deep vein thrombosis (DVT) of lower extremity., Methods: At the curse of disease from six hours to ninety days, one hundred and two patients with DVT including one hundred and three lower extremities had received surgical procedure and intravascular minimal invasive treatment., Results: There were not procedure-related morbidities in 102 cases, and symptoms disappeared, all procedures were successful based on angiography. The detecting head for the intravascular ultrasound ablation was entered to inferior vena cava (IVC) in 74 cases (78%), Forgarty catheter was entered to IVC in 21 cases (21%), the stenosis in the confluence of the common iliac vein and IVC was dilated by sacculus rotundus catheter in 89 cases (88%), including 9 patients underwent percutaneous transluminal stenting. One hundred and two patients followed up for twenty months, follow-up by angiography showed no restenosis in 91 cases, restenosis in ilio-femoral vein in 1 cases, and thrombus recontouring in 4 cases, as well as 6 cases died caused by primary disease., Conclusion: Surgical procedure combined with the intravascular minimal invasive technique is a safe and effective therapeutic method for DVT.