‎in this paper we introduce mixed unitary cayley graph $m_{n}$‎ ‎$(n>1)$ and compute its eigenvalues‎. ‎we also compute the energy of‎ ‎$m_{n}$ for some $n$‎.

On-line multicasting has received a lot of attention lately, because of its great practical importance. However, most research assumes undirected graphs, which fail to model the directivity of real networks. In this paper, we ll this gap by ooering upper and lower bounds for the on-line directed multicast problem in a worst case analysis. We examine two types of on-line problems: the join-only ...

The vertex distance complement (VDC) matrix \(\textit{C}\), of a connected graph \(G\) with set consisting \(n\) vertices, is real symmetric \([c_{ij}]\) that takes the value \(n - d_{ij}\) where \(d_{ij}\) between vertices \(v_i\) and \(v_j\) for \(i \neq j\) 0 otherwise. spectrum subdivision join, \(G_1 \dot{\bigvee} G_2\) edge join \underline{\bigvee} regular graphs \(G_1\) \(G_2\) in terms ...

Given a graph G with weighted edges, and a subset of nodes T , the T -join problem asks for a minimum weight edge set A such that a node u is incident to an odd number of edges of A i u 2 T . We describe the applications of the T -join problem in sparse graphs to the phase assignment problem in VLSI mask layout and to conformal re nement of nite element meshes. We suggest a practical algorithm ...

Join ordering is the problem of finding cost optimal execution plans for matching multi-headed rules. In the context of Constraint Handling Rules, this topic has received limited attention so far, even though it is of great importance for efficient CHR execution. We present a formal cost model for joins and investigate the possibility of join optimization at runtime. We propose some heuristic a...