We consider some classical constructions of graphs: join of two graphs, duplication of a vertex, and show that they behave nicely from the point of view of the existence of kernels. c © 1999 Elsevier Science B.V. All rights reserved.

We introduce joins of signed graphs and explore the chromatic number all-positive all-negative joins. prove an analogue to theorem that join two equals sum their numbers. Given graphs, is usually less than numbers, by amount depends on new concept deficiency a signed-graph coloration.

Let $$G = (V,E)$$ be a connected simple graph of order p and size q. A G is called local antimagic if admits labeling. bijection $$f \colon E \to \{1,2,\ldots,q\}$$ labeling for any two adjacent vertices $$u$$ $$v$$ , we have $$f^+(u) \ne f^+(v)$$ where \sum_{e\in E(u)} f(e)$$ $$E(u)$$ the set edges incident to . Thus, induces proper vertex coloring assigned color $$f^+(v)$$ The chromatic numbe...

This study deals with the forcing subsets of a minimum connected co-independent hop dominating sets in graphs. Bounds or exact values domination numbers graphs resulting from some binary operations such asjoin and corona are determined.Some main results generated this include characterization sets, for these types bounds join

In this paper, we provide an upper bound for the intersection number in join and corona of graphs. Moreover, give formulas Kn ◦G, Pn Cn ◦G Crn.

In this paper we determine when the join of two graphs is locally homogeneous. It is shown that the Cartesian product of a locally H1 graph and a locally H2 graph is locally (H1∪ H2). All graphs H of order at most 4 for which there are no locally H graphs are determined.