# On the Strong Rainbow Connection of a Graph

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An edge of a k-connected graph G is said to be k-removable if G âˆ’ e is still k-connected. A subgraph H of a k-connected graph is said to be k-contractible if its contraction, that is, identification every component of H to a single vertex, results again a k-connected graph. In this paper,...

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The concept of triple connected graphs with real life application was introduced in [7] by considering the existence of a path containing any three vertices of a graph G. In this paper, we introduce a new domination parameter, called Smarandachely triple connected domination number of a graph. A...

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A vertex-colored graph G is rainbow vertex-connected if any two vertices are connected by a path whose internal vertices have distinct colors. The rainbow vertex-connection number of a connected graph G, denoted by rvc(G), is the smallest number of colors that are needed in order to make G...

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In this paper, we introduce and investigate the connected open monophonic sets and related parameters. For a connected graph G of order n, a subset S of vertices of G is a monophonic set of G if each vertex v in G lies on a x-y monophonic path for some elements x and y in S. The minimum...

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Let S be a bipartite semigraph with NXa(y) â‰¥ 1 for every y âˆˆ Y . A vertex x âˆˆ X hyper dominates y âˆˆ Y if y âˆˆ Na(x) or y âˆˆ Na(NYa(x)). A subset D âŠ† X is a hyper dominating set of S if every y âˆˆ Y is hyper dominated by a vertex of D. A subset D âŠ† X...

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Let G = ( V ( G), E( G)) be a simple graph. A subset S of V ( G) is a dominating set of G if, for any vertex v âˆˆ V ( G) - S, there exists some vertex u âˆˆ S such that uv âˆˆ E( G). The domination number, denoted by Î³( G), is the cardinality of a minimal dominating set of G. There...

- ON THE MAXIMUM ORDERS OF AN INDUCED FOREST, AN INDUCED TREE, AND A STABLE SET. HERTZ, Alain; MARCOTTE, Odile; SCHINDL, David // Yugoslav Journal of Operations Research;2014, Vol. 24 Issue 2, p199
Let G be a connected graph, n the order of G, and f (resp. t) the maximum order of an induced forest (resp. tree) in G. We show that f - t is at most n - âŒˆ2âˆšn - 1âŒ‰. In the special case where n is of the form aÂ² + 1 for some even integer a â‰¥ 4, f - t is at most n -...

- On edge neighborhood graphs-II. Alsardary, Salar Y.; All, Ali A.; Balasubramanian, K. // Azerbaijan Journal of Mathematics;Jul2012, Vol. 2 Issue 2, p78
Let G be an undirected, simple, connected graph e and e = uv be an edge of G: Let NG(e) be the subgraph of G induced by the set of all vertices of G which are not incident to e but are adjacent to at least one end vertex of e. Ne is the class of all graphs H such that, for some graph G, NG(e)...