Join of Two Graphs
Distinguishing Number and Distinguishing Index of the Join of Two Graphs
... The distinguishing number (index) D(G) (D 0 (G)) of a graph G is the least integer d such that G has an vertex labeling (edge labeling) with d labels that is preserved only by a trivial automorphism. In this paper we ...
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Vol 8, No 7 (2017)
... L et πΊ be a connected simple graph. A restrained convex dominating set π in a connected graph πΊ is a secure restrained convex dominating set, if for each element π’ in π(πΊ)\π there exists an element π£ in π such that π’π£ β ...
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Upper Distance k-Cost Effective Number in the Join of Graphs
... maximum cardinality of a distance k- cost effective set of G is called the upper distance k- cost effective number of G. In this paper, we characterized a distance k- cost effective set in the join of two ...
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Observations Concerning Chordal Graph Polynomials
... for graphs that are clique equivalent to connected chordal graphs β or for graphs that are the join of two graphs, at least one of which is clique equivalent to a connected ...
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On Strong Resolving Domination in the Join and Corona of Graphs
... the join of two graphs G and H, the previous results have already considered the case when G or H is ...the join of nontrivial connected graphs G and H is ...
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Vol 10, No 6 (2019)
... The join of two graphs G and H , denoted by G + H , is the graph with vertex set V ( G + H ) = V ( G ) βͺ ο¦ V ( H ) and edge set E ( G + H ) = E ( G ) βͺ ο¦ E ( H ) βͺ ο¦ { uv : u β V ( G ), v β V ( H )} ...
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Vertex Distance Complement Spectra of Some Graphs
... of graphs. We mainly discuss the VDC - spectrum of join of two graphs, Cartesian product, double graph, lexicographic product, double odd graph and extended double cover ...some graphs ...
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Non split and Inverse Non split Domination Numbers in the Join and Corona of Graphs
... is connected, then D 0 is called an inverse non-split dominating set. The inverse non-split domination number of G is the minimum cardinality of an inverse non-split dominating set in G . In this paper, characterization ...
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On common neighborhood graphs II
... HajΓ³s join which is introduced in [11]. Let and be two graphs, β ( ), and β ( ...HajΓ³s join of these two graphs, which is denoted by β ,is a new graph that combines the ...
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On Semitotal Domination in Graphs
... Given two graphs G and H with disjoint vertex sets, the join of G and H is the graph G+H with V (G+H) = V (G)βͺV (H) and E(G +H) = E(G)βͺ E(H) βͺ{uv : u β V (G), v β V ...these graphs, G and H ...
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Vol 6, No 11 (2015)
... . Two graphs πΊπΊ 1 and πΊπΊ 2 are said to be Harary equienergetic if π»π»π»π»(πΊπΊ 1 ) = π»π»π»π»(πΊπΊ 2 ) ...the join of regular graphs of diameter less than or equal to two and thus construct the ...
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Generalized Degree Distance of Strong Product of Graphs
... bicyclic graphs are studied by Hamzeh ...product, join, symmetric difference, composition and disjunction of two ...many graphs arise from simpler graphs via various graph ...product ...
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The Endomorphism Monoids of (n β 3)-regular Graphs of Order n
... the join of graphs is regular, then each endomorphism of the graphs is regular, and for any graph G, the endo- morphism monoid of G is regular if and only if the endomorphism monoid of the ...
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Some Results on Generalized Degree Distance
... composition, join, dis- junction and symmetric difference of graphs and introduce generalized and modified generalized degree distance poly- nomials of graphs, such that their first derivatives at x ...
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Edge domination in fuzzy graphs using strong arcs
... Proof. Let π· = {π’ 1 , π’ 2 , β¦ . . π’ π } be a minimum strong vertex dominating set of G. Arrange the elements of D such that π π (π’ π ) β€ π π (π’ π+1 ). Since D is minimal, π π (π’ π ) β 0 for 1 β€ π β€ π. Also, since β(πΊ) β€ ...
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On Topologies Induced by Graphs Under Some Unary and Binary Operations
... Let G = (V (G), V (H)) be any simple undirected graph. The distance d(u, v) be- tween two vertices u and v in G is the length of a shortest path joining u and v. Let v β V (G). The neighborhood of v is the set N ...
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A note on the power graph of a finite group
... power graphs. Moghaddamfar et al. [15] considered the proper power graph P β (G). This graph can be constructed from P (G) by deleting the identity element of G. They provided necessary and suο¬cient conditions for ...
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Balanced Degree-Magic Labelings of Complete Bipartite Graphs under Binary Operations
... magic graphs was introduced by SedlΒ΄ aΛ cek [8]. Later, su- permagic graphs were introduced by Stewart ...supermagic graphs; see [6, 7, 10] for more comprehen- sive ...degree-magic graphs was ...
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On the classification problem for split graphs
... 1. Graphs whose chromatic index is equal to are said to be Class 1; graphs whose chro- matic index is equal to + 1 are said to be Class ...of graphs such as per- fect ...of graphs that include ...
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Total Partial Domination in Graphs Under Some Binary Operations
... the join, corona, lexico- graphic product and Cartesian product of graphs are found in Macapodi et ...connected graphs of orders m and n, respectively, and let Ξ± β (0, ...
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