The concept of super line graph was introduced in the year 1995 by Bagga, Beineke and Varma. Given a graph with at least r edges, the super line graph of index r, Lr(G), has as its vertices the sets of r-edges of G, with two adjacent if there is an edge in one set adjacent to an edge in the other set. The line completion number lc(G) of a graph G is the least positive integer r for which Lr(G) ...

The underlying theme of this paper is to explore the various facets power systems data through lens graph signal processing (GSP), laying down foundations Grid-GSP framework. provides an interpretation for spatio-temporal properties voltage phasor measurements, by showing how well-known modeling supports a generative low-pass filter model state variables, namely phasors. Using we formalize empi...

let g(v,e) be a graph with p vertices and q edges. a graph g is said to have an odd mean labeling if there exists a function f : v (g) → {0, 1, 2,...,2q - 1} satisfying f is 1 - 1 and the induced map f* : e(g) → {1, 3, 5,...,2q - 1} defined by f*(uv) = (f(u) + f(v))/2 if f(u) + f(v) is evenf*(uv) = (f(u) + f(v) + 1)/2 if f(u) + f(v) is odd is a bijection. a graph that admits an odd mean lab...

in this paper, the weighted szeged indices of cartesian product and corona product of twoconnected graphs are obtained. using the results obtained here, the weighted szeged indices ofthe hypercube of dimension n, hamming graph, c4 nanotubes, nanotorus, grid, t− fold bristled,sunlet, fan, wheel, bottleneck graphs and some classes of bridge graphs are computed.

One of the well-known NP-complete problems in graph theory is the Hamiltonian path problem; i.e., finding a simple path in the graph such that every vertex visits exactly once [5]. The two-dimensional integer grid G is an infinite undirected graph in which vertices are all points of the plane with integer coordinates and two vertices are connected by an edge if and only if the Euclidean distanc...

A triangular grid graph is a finite induced subgraph of the infinite graph associated with the two-dimensional triangular grid. We show that the problem Hamiltonian Cycle is NP-complete for triangular grid graphs, while a hamiltonian cycle in connected, locally connected triangular grid graph can be found in polynomial time. 2000 Mathematics Subject Classification: 05C38 (05C45, 68Q25).

A grid graph is a nite node-induced subgraph of the innnite two-dimensional integer grid. A solid grid graph is a grid graph without holes. For general grid graphs, the Hamiltonian cycle problem is known to be NP-complete. We give a polynomial-time algorithm for the Hamiltonian cycle problem in solid grid graphs, resolving a longstanding open question posed in IPS82]. In fact, our algorithm can...