We consider the problems of completing a low-rank positive semidefinite square matrix M or a low-rank rectangular matrix N from a given subset of their entries. Following the approach initiated by Singer and Cucuringu [20] we study the local and global uniqueness of such completions by analysing the structure of the graphs determined by the positions of the known entries of M or N . We present ...

Todeschini et al. have recently suggested to consider multiplicative variants of additive graph invariants, which applied to the Zagreb indices would lead to the multiplicative Zagreb indices of a graph G, denoted by ( ) 1  G and ( ) 2  G , under the name first and second multiplicative Zagreb index, respectively. These are define as     ( ) 2 1 ( ) ( ) v V G G G d v and ( ) ( ) ( ) ( ) 2...

In this paper, we compute the formulae for the third Zagreb indices and its coindices for two classes of graphs such as edge corona product graph, double graph and kth iterated double graph.

An arc-representation of a graph is a function mapping each vertex in the graph to an arc on the unit circle in such a way that adjacent vertices are mapped to intersecting arcs. The width of such a representation is the maximum number of arcs passing through a single point. The arc-width of a graph is defined to be the minimum width over all of its arc-representations. We extend the work of Ba...

We present here prime cordial labeling for the graphs obtained by some graph operations on cycle related graphs.

In this article we study the modular product graph operation, denoted by ♦, with particular emphasis on when the operation preserves the property of a graph being 3-existentially closed. We characterise when G♦H is 3e.c. provided that H is 3-e.c., and we establish two new infinite classes of 3-e.c. graphs of the form G♦H, for which G need not be 3-e.c. itself.

The F-index of a graph is defined as the sum of cubes of the vertex degrees of the graph which was introduced in 1972, in the same paper where the first and second Zagreb indices were introduced. In this paper we study the F-index of four operations on graphs which were introduced by Eliasi and Taeri [M. Eliasi, B. Taeri, Four new sums of graphs and their Wiener indices, Discrete Appl. Math.157...

The corona product G ◦ H of two graphs G and H is obtained by taking one copy of G and |V (G)| copies of H; and by joining each vertex of the i-th copy of H to the i-th vertex of G, where 1 ≤ i ≤ |V (G)|. In this paper, exact formulas for the eccentric distance sum and the edge revised Szeged indices of the corona product of graphs are presented. We also study the conditions under which the cor...