The Grundy domination number, γgr(G), of a graph G is the maximum length sequence (v1,v2,…,vk) vertices in such that for every i∈{2,…,k}, closed neighborhood N[vi] contains vertex does not belong to any N[vj], where j<i. It well known number greater than or equal upper Γ(G), which turn independence α(G). In this paper, we initiate study class graphs with Γ(G)=γgr(G) and its subclass consisting ...

Related DatabasesWeb of Science You must be logged in with an active subscription to view this.Article DataHistorySubmitted: 15 March 2021Accepted: 27 September 2021Published online: 10 January 2022Keywordsindependence number, resilience, Erdös--Rogers functionAMS Subject Headings05C69, 05C55Publication DataISSN (print): 0895-4801ISSN (online): 1095-7146Publisher: Society for Industrial and App...

An independent broadcast on a graph G is function f : V −→ {0,. .. , diam(G)} such that (i) (v) ≤ e(v) for every vertex v ∈ (G), where diam(G) denotes the diameter of and eccentricity v, (ii) d(u, v) > max{f (u), (v)} two distinct vertices u with (u)f 0. The independence number β b (G) then maximum value v∈V (v), taken over all broadcasts G. We prove circulant form C(n; 1, a), 3 ⌊ n 2 ⌋, admits...

Given a digraph D with m arcs and bijection τ:A(D)→{1,2,…,m}, we say (D,τ) is an antimagic orientation of graph G if no two vertices in have the same vertex-sum under τ, where vertex u τ sum labels all entering minus leaving u. Hefetz, Mütze, Schwartz 2010 initiated study orientations graphs, conjectured that every connected admits orientation. This conjecture seems hard, few related results ar...

The goal of this paper is to find vertex disjoint even cycles in graphs. For this purpose, define a θ-graph to be a pair of vertices u, v with three internally disjoint paths joining u to v. Given an independence number α and a fixed integer k, the results contained in this paper provide sharp bounds on the order f(k, α) of a graph with independence number α(G) ≤ α which contains no k disjoint ...

In this paper, we deal with the independence number of iterated line digraphs of a regular digraph G. We give pertinent lower bounds and give an asymptotic estimation of the ratio of the number of vertices of a largest independent set of the nth iterated line digraph of G. © 2005 Elsevier B.V. All rights reserved.

By using the notion of compatibility of subgraphs with a perfect matching developed for digraphs in [1], we show that if, in a balanced bipartite graph G of minimum degree 6, the maximum cardinality ebip of a balanced independent subset satisfies ~bip ~< 26-4, then G is hamiltonian-biconnected, and if Ctbip ~< 26-2, G contains a hamiltonian path. Moreover, we give some properties of balanced bi...

For finite graphs F and G, let Nr(G) denote the number of occurrences of F in G, i.e., the number of subgraphs of G which are isomorphic to F. I f g and c?? are families of graphs, it is natural to ask then whether or not the quantities NF(G), FE F, are linearly independent when G is restricted to Q. For example, if P = (K1, &} (where K, denotes the complete graph on n vertices) and 9 is the fa...

For a non-negative integer T , we prove that the independence number of a graph G = (V,E) in which every vertex belongs to at most T triangles is at least ∑ u∈V f(d(u), T ) where d(u) denotes the degree of a vertex u ∈ V , f(d, T ) = 1 d+1 for T ≥ ( d 2 ) and f(d, T ) = (1 + (d2− d− 2T )f(d− 1, T ))/(d2 + 1− 2T ) for T < ( d 2 ) . This is a common generalization of the lower bounds for the inde...