In the present paper, we introduce classical mean labeling of graphs and investigate their related properties. Moreover, it is obtained that line graph operation preserves meanness property for some standard graphs.

We explore an operation on graphs that is analogous to the factorial of a positive integer. We develop formulas for the factorials of complete graphs, odd cycles and complete bipartite graphs, and we prove some properties of the factorial operation. We conclude with a list of open questions. This paper explores some properties of a factorial operation that associates to each graph G a graph G! ...

We give an eecient algorithm for maintaining a minimum spanning forest of a plane graph subject to on-line modiications. The modii-cations supported include changes in the edge weights, and insertion 1 and deletion of edges and vertices which are consistent with the given embedding. To implement the algorithms, we develop a data structure called an edge-ordered dynamic tree, which is a variant ...

We consider principal pivot transform (pivot) on graphs. We define a natural operation, called dual pivot, and show that both the kernel and the set of maximally applicable pivots of a graph is invariant under this operation. The result is motivated by and applicable to the theory of gene assembly in ciliates.

In computer science, dependence analysis determines whether or not it is safe to parallelize statements in programs. In dealing with the data-intensive and computationally intensive spatial operations in processing massive volumes of geometric features, this dependence can be well utilized for exploiting the parallelism. In this paper, we propose a graph-based divide and conquer method for para...

the order graph of a group $g$, denoted by $gamma^*(g)$, is a graph whose vertices are subgroups of $g$ and two distinct vertices $h$ and $k$ are adjacent if and only if $|h|big{|}|k|$ or $|k|big{|}|h|$. in this paper, we study the connectivity and diameter of this  graph. also we give a relation between the order graph and prime  graph of a group.

let f, g and h be non-empty graphs. the notation f → (g,h) means that if any edge of f is colored by red or blue, then either the red subgraph of f con- tains a graph g or the blue subgraph of f contains a graph h. a graph f (without isolated vertices) is called a ramsey (g,h)−minimal if f → (g,h) and for every e ∈ e(f), (f − e) 9 (g,h). the set of all ramsey (g,h)−minimal graphs is denoted by ...

One of the most common ways of representing classes of equivalent Bayesian networks is the use of essential graphs. These chain graphs are also known in the literature as completed patterns or completed pdags. The name essential graph was proposed by Andersson, Madigan and Perlman (1997a) who also gave a graphical characterization of essential graphs. In this contribution an alternative charact...

In this paper, we propose a novel tensor graph convolutional neural network (TGCNN) to conduct convolution on factorizable graphs, for which here two types of problems are focused, one is sequential dynamic graphs and the other is cross-attribute graphs. Especially, we propose a graph preserving layer to memorize salient nodes of those factorized subgraphs, i.e. cross graph convolution and grap...

A graph G is 3-domination critical if its domination number γ is 3 and the addition of any edge decreases γ by 1. It was proved by Favaron et al. that α ≤ δ + 2 for any connected 3-domination critical graph. Denote by τ (G) the toughness of a graph G . Recently Chen et al. conjectured that a connected 3-domination critical graph G is Hamilton-connected if and only if τ (G) > 1 and showed the co...