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) ...

Let C be a finite connected graph for which there is a countable universal C-free graph, and whose tree of blocks is a path. Then the blocks of C are complete. This generalizes a result of Füredi and Komjáth, and fits naturally into a set of conjectures regarding the existence of countable C-free graphs, with C an arbitrary finite connected graph.

The Wiener index of a strong digraph D is defined as the sum shortest path distances between all ordered pairs vertices. This definition has been extended to digraphs that are not necessarily by defining distance from vertex b 0 if there no in D. Knor et al. (2016) [9] considered (not strong) orientations graphs with maximum index. authors conjectured for given tree T, an orientation T always c...

a compact formulation of the set of tours neither in a graph nor its complement is presented and illustrates a general methodology proposed for constructing polyhedral models of decision problems based upon permutations, projection and lifting techniques. directed hamilton tours on n vertex graphs are interpreted as (n-1)- permutations. sets of extrema of birkhoff polyhedra are mapped to tours ...

Background: In recent years, there has been an increase in the amount and variety of data generated in the field of healthcare, (e.g., data related to the prevalence of contagious diseases in the society). Various patterns of individuals’ relationships in the society make the analysis of the network a complex, highly important process in detecting and preventing the incidence of diseases....

Let $R$ be a commutative ring with identity and let $M$ be an $R$-module. In this paper we introduce a new graph associated to modules over commutative rings. We study the relationship between the algebraic properties of modules and their associated graphs. A topological characterization for the completeness of the special subgraphs is presented. Also modules whose associated graph is complete...

Let f(n, H) denote the maximum number of copies H possible in an n-vertex planar graph. The function has been determined when is a cycle length 3 or 4 by Hakimi and Schmeichel complete bipartite graph with smaller part size 1 2 Alon Caro. We determine exactly case path 3.

In this paper we generalize the remainder cordial labeling, called $k$-remainder cordial labeling and investigate the $4$-remainder cordial labeling behavior of certain graphs.

The main aim of this study is to characterize new classes of multicone graphs which are determined by their signless Laplacian spectra. A multicone graph is defined to be the join of a clique and a regular graph. Let C and K w denote the Clebsch graph and a complete graph on w vertices, respectively. In this paper, we show that the multicone graphs K w ▽C are determined by their signless ...