let g be a (p,q) graph. an injective map f : e(g) → {±1,±2,...,±q} is said to be an edge pair sum labeling if the induced vertex function f*: v (g) → z - {0} defined by f*(v) = σp∈ev f (e) is one-one where ev denotes the set of edges in g that are incident with a vertex v and f*(v (g)) is either of the form {±k1,±k2,...,±kp/2} or {±k1,±k2,...,±k(p-1)/2} u {±k(p+1)/2} according a...

We propose a generalization of the notion of R-split mixed Hodge structure by defining a Rsplitting level for mixed Hodge structures. This is a discrete invariant taking values in positive integers and equal to 0 for R-split mixed Hodge structures. We describe some properties of this invariant for classical operations on these structures and give some explicit calculation. Résumé Nous proposons...

For improving the reliability and efficiency of the kineto-static analysis of complex robot systems, the corresponding vector bond graph procedure is proposed. By the kinematic constraint condition, the vector bond graph model of universal joint are made. Based on this, the vector bond model of 3-RRRT parallel Manipulator is built. For solving the algebraic difficulties brought by differential ...

Many variants of pseudo-cliques have been introduced as relaxation models of cliques to detect communities in real world networks. For most types of pseudo-cliques, enumeration algorithms can be designed just similar to maximal clique enumerator. However, the problem of enumerating pseudo-cliques are computationally hard, because the number of maximal pseudo-cliques is huge in general. Furtherm...

A graph G is a fractional ( , b k )-critical covered if − U [ ]-covered for every ⊆ V ) with | = which first defined by (Zhou, Xu and Sun, Inf. Process. Lett. 152 (2019) 105838). Furthermore, they derived degree condition to be graph. In this paper, we gain an independence number connectivity verify that ≥ max {2 +1)( +1)+4 bk +5/4 ,( +1) 2

A homogeneous set is a non-trivial module of a graph, i.e. a nonempty, non-unitary, proper subset of a graph’s vertices such that all its elements present exactly the same outer neighborhood. Given two graphs G1(V, E1), G2(V, E2), the Homogeneous Set Sandwich Problem (HSSP) asks whether there exists a sandwich graph GS(V, ES), E1 ⊆ ES ⊆ E2, which has a homogeneous set. In 2001, Tang et al. [15]...

A derived graph is a obtained from given according to some predetermined rules. Two of the most frequently used graphs are line and total graph. Calculating properties helps calculate same original For this reason, relations between its always welcomed. recently introduced index which also acts as invariant called omega obtain such for graphs. As an illustrative exercise, values number faces cl...

We formulate weighted graph clustering as a prediction problem1: given a subset of edge weights we analyze the ability of graph clustering to predict the remaining edge weights. This formulation enables practical and theoretical comparison of different approaches to graph clustering as well as comparison of graph clustering with other possible ways to model the graph. We adapt the PAC-Bayesian ...