منابع مشابه
Distinct edge geodetic decomposition in graphs
Let G=(V,E) be a simple connected graph of order p and size q. A decomposition of a graph G is a collection π of edge-disjoint subgraphs G_1,G_2,…,G_n of G such that every edge of G belongs to exactly one G_i,(1≤i ≤n). The decomposition 〖π={G〗_1,G_2,…,G_n} of a connected graph G is said to be a distinct edge geodetic decomposition if g_1 (G_i )≠g_1 (G_j ),(1≤i≠j≤n). The maximum cardinality of π...
متن کاملSampling Edge Covers in 3-Regular Graphs
An edge cover C of an undirected graph is a set of edges such that every vertex has an adjacent edge in C. We show that a Glauber dynamics Markov chain for edge covers mixes rapidly for graphs with degrees at most three. Glauber dynamics have been studied extensively in the statistical physics community, with special emphasis on lattice graphs. Our results apply, for example, to the hexagonal l...
متن کاملSigned (b, k)-Edge Covers in Graphs
Let be a simple graph with vertex set and edge set . Let have at least vertices of degree at least , where and b are positive integers. A function is said to be a signed -edge cover of G if G ( ) V G ( ) e E v ( ) E G G : ( f E k b k ) { 1,1} G ( , ) b k ( ) f e b for at least vertices of , where . The value k v G ( ) = {uv E( ( ) E v G u N v ) | } ( ) min ( ) G e E f e , taki...
متن کاملOn the edge geodetic and edge geodetic domination numbers of a graph
In this paper, we study both concepts of geodetic dominatingand edge geodetic dominating sets and derive some tight upper bounds onthe edge geodetic and the edge geodetic domination numbers. We also obtainattainable upper bounds on the maximum number of elements in a partitionof a vertex set of a connected graph into geodetic sets, edge geodetic sets,geodetic domin...
متن کاملSigned B-edge Covers of Graphs
We study a signed variant of edge covers of graphs. Let b be a positive integer, and let G be a graph with minimum degree at least b. A signed b-edge cover of G is a function f : E(G) → {−1, 1} satisfying e∈EG(v) f(e) ≥ b for every v ∈ V (G). The minimum of the values of e∈E(G) f(e), taken over all signed b-edge covers f of G, is called the signed b-edge cover number and is denoted by ρb(G). Fo...
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ژورنال
عنوان ژورنال: Proyecciones (Antofagasta)
سال: 2015
ISSN: 0716-0917
DOI: 10.4067/s0716-09172015000400003