Recently, complementary perfect corona domination in graphs was introduced. A dominating set S of a graph G is said to be (CPCD – set) if each vertex either pendent or support and has matching. The minimum cardinality called the number denoted by . In this paper, our parameter hasbeen discussed for power path cycle.

While representation learning has yielded a great success on many graph tasks, there is little understanding behind the structures that are being captured by these embeddings. For example, we wonder if topological features, such as Triangle Count, Degree of node and other centrality measures concretely encoded in Furthermore, ask presence embeddings necessary for better performance downstream c...

In a non-complete graph $Gamma$, a vertex triple $(u,v,w)$ with $v$ adjacent to both $u$ and $w$ is called a $2$-geodesic if $uneq w$ and $u,w$ are not adjacent. The graph $Gamma$ is said to be   $2$-geodesic transitive if its automorphism group is transitive on arcs, and also on 2-geodesics. We first produce a reduction theorem for the family of $2$-geodesic transitive graphs of prime power or...

The automatic identification of the topology power networks is important for data-driven and situation-aware operation grids. Traditional methods lack a data-tolerant mechanism, accuracy their performance in terms thus affected by quality data. Topology related to link prediction problem. graph neural network can be used predict state unlabeled nodes (lines) through training on features labeled...

The k-power graph of a graph G is a graphwith the same vertex set as G, in that two vertices are adjacent if and only if, there is a path between them in G of length at most k. A k-treepower graph is the k-power graph of a tree, a k-leaf-power graph is the subgraph of some k-tree-power graph induced by the leaves of the tree. We show that (1) every k-tree-power graph has NLC-width at most k + 2...

Clique-width is a graph parameter with many algorithmic applications. For a positive integer k, the k-th power of a graph G is the graph with the same vertex set as G, in which two distinct vertices are adjacent if and only if they are at distance at most k in G. Many graph algorithmic problems can be expressed in terms of graph powers. We initiate the study of graph classes of power-bounded cl...