This study deals primarily with the connected closed geodetic numbers of some graphs, a closed geodetic closure invariant introduced by Buckley and Harary [2]. For S ⊆ V (G), where G is a connected graph, the geodetic closure I G [S] of S is the set of all vertices lying on some u-v geodesic where u and v are in S. In this paper, select vertices of G sequentially as follows: Select a vertex v 1 and let S 1 = {v 1 }. Select a vertex v 2 = v 1 and let S 2 = {v 1 , v 2 }, then determine I G [S 2 ]. If I G [S 2 ] = V (G), then successively select vertex v i / ∈ I G [S i−1 ] and let S i = {v 1 , v 2 , ..., v i } for i = 1, 2, ..., k. Then determine I G [S i ]. The connected closed geodetic number of a graph, denoted by ccgn(G), is defined to be the smallest k whose selection of v k in the given manner yields I G [S k ] = V (G), where S is connected. In this paper, the connected closed geodetic numbers of some graphs and the join of some connected graphs G and H were determined.

This study deals primarily with the connected closed geodetic numbers of the join of two graphs which is a modification of the closed geodetic number of graphs studied by Aniversario in [2], a geodetic closure invariant introduced by Buckley and Harary in [4]. The concept of connected closed geodetic number of a graph G, denoted by ccgn(G) is introduced and some of its properties are investigated. It is proved that, if G is a connected graph with cut-vertices and if S is a connected closed geodetic basis of G, such that w is a cut-vertex of G, then each component of G-w contains an element of S. It is shown that every cut-vertex of a connected graph G belongs to every connected closed geodetic basis of G. Some connected graphs G for which the ccgn is equal to p and 2 are characterized. In this paper, the concept of a 2-path connected closure of S in a graph G, denoted by P c 2 [S] G , is introduced. Likewise, the properties of connected closed geodetic basis of a graph G resulting from the join of connected graphs H and K for which K is a complete graph and of connected graphs H and K for which K is not a complete graph are investigated and the ccgn of G is also determined.

Given a graph G and a configuration C of pebbles on the vertices of G, a pebbling step or move [u, v] consists of removing two pebbles off of one vertex u, and then placing one pebble on an adjacent vertex v. In a pebbling step [u, v], u is the support vertex while v is a target vertex. A graph is said to be cover-pebbled if every vertex has a pebble on it after a series of pebbling steps. The cover pebbling number γ(G) of a graph G is the minimum number of pebbles such that however the pebbles are initially placed on the vertices of G we can eventually put a pebble on every vertex simultaneously by a pebbling step. In this paper, the cover pebbling number of graphs resulting from the join of two graphs G and H are determined via a key vertex of the graph. In particular, this paper determines the cover pebbling number of the wheels W n , the fans F n , and the join of any graph G with P n and C n , respectively

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Dengue is a viral mosquito-borne infection transmitted primarily by the Aedes mosquitoes. It is one of the several emerging tropical diseases which progressively spread geographically to virtually all tropical countries like the Philippines. Recent climate changes related to global warming have increased the potential risk of dengue outbreaks in the world. In this paper, we study and investigate temperature and precipitation as climatological factors affecting dengue incidence in the Philippines from the year 2015 to 2018. Monthly dengue cases and climate data were gathered for the said study period. A correlation and wavelet coherence analyses were performed to determine a relationship between dengue incidence and climatological factors in the Philippines. Results show that the amount of rainfall is strongly correlated to the increase of dengue cases in the country as compared to the temperature. Evidence shows that dengue incidence in the Philippines mostly occur during the rainy season. Thus, intensified surveillance and control of mosquitoes during the rainy season are recommended.