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...

My research involves finding bounds of graph theoretic invariants, in particular the independence number of a graph; constructing algorithms for calculating values of these invariants; investigating the structure of independent sets of vertices in graphs; and identifying and programming successful heuristics for automating conjecture-making. of these conjectures have involved the independence n...

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 ...