Temporal graphs naturally model whose underlying topology changes over time. Recently, the problems Vertex Cover (or TVC) and Sliding-Window Delta-TVC for time-windows of a fixed-length Delta) have been established as natural extensions classic problem on static with connections to areas such surveillance in sensor networks. In this paper we initiate systematic study complexity TVC sparse graph...

A preferential attachment model for a growing network incorporating deletion of edges is studied and the expected asymptotic degree distribution is analyzed. At each time step t = 1, 2, . . ., with probability π1 > 0 a new vertex with one edge attached to it is added to the network and the edge is connected to an existing vertex chosen proportionally to its degree, with probability π2 a vertex ...

A preferential attachment model for a growing network incorporating deletion of edges is studied and the expected asymptotic degree distribution is analyzed. At each time step t = 1, 2, . . ., with probability π1 > 0 a new vertex with one edge attached to it is added to the network and the edge is connected to an existing vertex chosen proportionally to its degree, with probability π2 a vertex ...

the eccentricity connectivity index of a molecular graph g is defined as (g) = av(g)deg(a)ε(a), where ε(a) is defined as the length of a maximal path connecting a to othervertices of g and deg(a) is degree of vertex a. here, we compute this topological index forsome infinite classes of dendrimer graphs.

The first and second Zagreb indices of a graph are equal, respectively, to the sum of squares of the vertex degrees, and the sum of the products of the degrees of pairs of adjacent vertices. We now consider analogous graph invariants, based on the second degrees of vertices (number of their second neighbors), called leap Zagreb indices. A number of their basic properties is established.

The energy E(G) of a graph G is equal to the sum of the absolute values of the eigenvalues of G. Several classes of graphs are known that satisfy the condition E(G) > n , where n is the number of vertices. We now show that the same property holds for (i) biregular graphs of degree a b , with q quadrangles, if q<= abn/4 and 5<=a < b = 0 (iii) triregular graphs of degree 1, a, b that are quadran...

A n-vertex graph is said to be decomposable if for any partition (λ1, . . . , λp) of the integer n, there exists a sequence (V1, . . . , Vp) of connected vertex-disjoint subgraphs with |Vi| = λi. In this paper, we focus on decomposable trees. We show that a decomposable tree has degree at most 4. Moreover, each degree-4 vertex of a decomposable tree is adjacent to a leaf. This leads to a polyno...

Let G be a simple graph with vertex set V and edge set E. The number of vertices of G is called the order, and is denoted by n = n(G). The open neighborhood N(v) = NG(v) of a vertex v consists of all vertices adjacent to v and d(v) = dG(v) = |N(v)| is the degree of v. The closed neighborhood of a vertex v is defined by N [v] = NG [v] = NG (v)∪{v}. By ∆ = ∆(G), we denote the maximum degree of th...

Abstract. The L(2, 1)-labeling (or distance two labeling) of a graph G is an integer labeling of G in which two vertices at distance one from each other must have labels differing by at least 2 and those at distance two must differ by at least 1. The L(2, 1)labeling numberλ G of G is the smallest number k such that G has an L(2, 1)-labeling max{ ( ): ( )} f v v V G k ∈ = with max f v : v V G k....

We give a sharp refinement of a result of Alon, Ben-Shimon and Krivelevich. This gives a sufficient condition for a finite sequence of positive integers to be the vertex degree list of both parts of a bipartite graph. The condition depends only on the length of the sequence and its largest and smallest elements.