Results 21 to 30 of about 11,572,072 (152)
On Equality and Strong Equality of Domination Number and Independent Domination Number in Graphs [PDF]
, 2021 In this paper we explore graphs having same domination number and independent domination number . Such graphs are denoted as ( , )-graphs. Several families of ( , )-graphs have been constructed.
Femlin, Pious, Mayamma, Joseph
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The Forcing Domination Number of Hamiltonian Cubic Graphs [PDF]
, 2009 The authors presented a sequence of Hamiltonian cubic graphs whose domination numbers are sharp and in this paper we study forcing domination number for those ...
H. Abdollahzadeh Ahangar +3 more
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On domination and independent domination numbers of a graph
Discrete Mathematics, 1978 AbstractFor a graph G, the definitions of domination number, denoted γ(G), and independent domination number, denoted i(G), are given, and the following results are obtained:Theorem. If G does not have an induced subgraph isomorphic to K1,3, then γ(G) = i(G).Corollary 1. For any graph G, γ(L(G))=i(L(G)), where L(G) is the line graph of G. (This extends
Robert B. Allan, Renu C. Laskar
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Triple Connected Domination Number of a Graph [PDF]
, 2012 The concept of triple connected graphs with real life application was introduced by considering the existence of a path containing any three vertices of a graph G.
Selvam Avadayappan +7 more
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Singed Total Domatic Number of a Graph [PDF]
, 2010 The maximum number of functions in a signed total dominating family on G is the signed total domatic number of G. In this paper, some properties related signed total domatic number and signed total domination number of a graph are studied and found the ...
Shailaja S. Shirkol +2 more
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The Number of Minimum Dominating Sets in Pn × P2 [PDF]
, 2010 A set S of vertices in a graph G is said to be a Smarandachely k-dominating set if each vertex of G is dominated by at least k vertices of S.
Kishori P. Narayankar +5 more
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On graphs with equal domination and independent domination numbers
Discrete Mathematics, 1991 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jerzy Topp, Lutz Volkmann
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Graphs with equal Grundy domination and independence number
Discrete Optimization, 2023 The Grundy domination number, ${γ_{\rm gr}}(G)$, of a graph $G$ is the maximum length of a sequence $(v_1,v_2,\ldots, v_k)$ of vertices in $G$ such that for every $i\in \{2,\ldots, k\}$, the closed neighborhood $N[v_i]$ contains a vertex that does not belong to any closed neighborhood $N[v_j]$, where ...
Gábor Bacsó +3 more
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On the Number of k‐Dominating Independent Sets [PDF]
Journal of Graph Theory, 2016 AbstractWe study the existence and the number of k‐dominating independent sets in certain graph families. While the case namely the case of maximal independent sets—which is originated from Erdős and Moser—is widely investigated, much less is known in general.
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Remarks on the outer-independent double Italian domination number [PDF]
, 2021 Let $G$ be a graph with vertex set $V(G)$. If $u \in V(G)$, then $N[u]$ is the closed neighborhood of $u$. An outer-independent double Italian dominating function (OIDIDF) on a graph $G$ is a function $ƒ : V(G) \rightarrow \{0, 1, 2, 3\}$ such that if $ƒ
Volkman, Lutz +2 more
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