<abstract><p>Gutman proposed the concept of Sombor index. It is defined via the term $ \sqrt{d_F(v_i)^2+d_F(v_j)^2} $, where $ d_F(v_i) $ is the degree of the vertex $ v_i $ in graph $ F $. Also, the reduced Sombor index and the Average Sombor index have been introduced recently, and these topological indices have good predictive potential in mathematical chemistry. In this paper, we determine the extreme molecular graphs with the maximum value of Sombor index and the extremal connected graphs with the maximum (reduced) Sombor index. Some inequalities relations among the chemistry indices are presented, these topology indices including the first Banhatti-Sombor index, the first Gourava index, the Second Gourava index, the Sum Connectivity Gourava index, Product Connectivity Gourava index, and Eccentric Connectivity index. In addition, we characterize the graph where equality occurs.</p></abstract>

The number of sudden cardiac death (SCD) has increased year by year, which has become one of the main causes of death in China. Timely cardiopulmonary resuscitation (CPR) and timely and accurate use of automatic external defibrillator (AED) can greatly improve the survival rate of patients with sudden cardiac death. Because the large probability of sudden cardiac death occurs outside the hospital, it is very important for the general public to master first aid skills. This paper will mine all kinds of data from multi-dimensional and multi-angle, analyze the mastery of public first aid skills in China, and provide practical suggestions and ideas for popularizing first aid skills in the future.

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Foucaud et al. recently introduced and initiated the study of a new graph-theoretic concept in the area of network monitoring. Let G = (V, E) be a graph. A set of vertices M ⊆ V (G) is a distance-edge-monitoring set of G if any edges in G can be monitored by a vertex in M . The distance-edge-monitoring number dem(G) is the minimum cardinality of a distance-edge-monitoring set of G. In this paper, we first show that dem(G \ e) − dem(G) ≤ 2 for any graph G and edge e ∈ E(G). Moreover, the bound is sharp. Next, we construct two graphs G and H to show that dem(G) − dem(G − u) and dem(H − v) − dem(H) can be arbitrarily large, where u ∈ V (G) and v ∈ V (H). We also study the relationship between dem(H) and dem(G) for H ⊂ G. In the end, we give an algorithm to judge whether the distance-edge-monitoring set still remain in the resulting graph when any edge of a graph G is deleted.

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