RESULTS ON MAJORITY DOM-CHROMATIC SETS OF A GRAPH
RESULTS ON MAJORITY DOM-CHROMATIC SETS OF A GRAPH
J. Joseline Manora, R. Mekala
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Abstract
A majority dominating set S ⊆ V (G) is said to be majority dominating chromatic set if S satisfies the condition χ(⟨S⟩) = χ(G). The majority dom-chromatic number γMχ(G) is the minimum cardinality of majority dominating chromatic set. In this article we investigated some inequalities on Majority dominating chromatic sets of a connected and disconnected graph G. Also characterization theorems and some results on majority dom-chromatic number γMχ(G) for a vertex color critical graph and biparte graph are determined. we established the relationship between three parameters namely χ(G),γM(G) and γMχ(G) for some graphs.
Keywords
Majority dominating set, Majority dominating chromatic set, Majority dom- chromatic number.
STRONGER RECONSTRUCTION OF DISTANCE-HEREDITARY GRAPHS
STRONGER RECONSTRUCTION OF DISTANCE-HEREDITARY GRAPHS
P. Devi Priya, S. Monikandan
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Abstract
Agraphissaidtobeset-reconstructibleifitisuniquelydetermineduptoiso- morphism from the set S of its non-isomorphic one-vertex deleted unlabeled subgraphs. Harary’s conjecture asserts that every finite simple undirected graph on four or more ver- tices is set-reconstructible. A graph G is said to be distance-hereditary if for all connected inducedsubgraphF ofG, dF(u,v)=dG(u,v)foreverypairofverticesu,v∈V(F).In this paper, we have proved that the class of all 2-connected distance-hereditary graphs G with diam(G) = 2 or diam(G) = diam(G) = 3 are set-reconstructible.
Keywords
Set-reconstruction, connectivity, distance, distance-hereditary
THE ORIENTATION NUMBER OF THREE COMPLETE GRAPHS WITH LINKAGES
THE ORIENTATION NUMBER OF THREE COMPLETE GRAPHS WITH LINKAGES
G. Rajasekaran, R. Sampathkumar
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Abstract
For a graph G, let D(G) be the set of all strong orientations of G. The orien- tation number of G is d(G) =min{d(D)|D ∈ D(G)}, where d(D) denotes the diameter of the digraph D. In this paper, we consider the problem of determining the orientation number of three complete graphs with linkages.
Keywords
complete graphs, orientation number
CYCLIC ORTHOGONAL DOUBLE COVERS OF 6-REGULAR CIRCULANT GRAPHS BY DISCONNECTED FORESTS
CYCLIC ORTHOGONAL DOUBLE COVERS OF 6-REGULAR CIRCULANT GRAPHS BY DISCONNECTED FORESTS
V. Sriram
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Abstract
An orthogonal double cover (ODC) of a graph H is a collection G = {Gv : v ∈ V (H)} of |V (H)| subgraphs of H such that every edge of H is contained in exactly two members of G and for any two members Gu and Gv in G, |E(Gu) ∩ E(Gv)| is 1 if u and v are adjacent in H and it is 0 if u and v are nonadjacent in H. An ODC G of H is cyclic if the cyclic group of order |V (H)| is a subgroup of the automorphism group of G; otherwise it is noncyclic. Recently, Sampathkumar and Srinivasan settled the problem of the existence of cyclic ODCs of 4-regular circulant graphs. An ODC G of H is cyclic (CODC) if the cyclic group of order |V(H)| is a subgroup of the automorphism group of G, the set of all automorphisms of G; otherwise it is noncyclic. In this paper, we have completely settled the existence problem of CODCs of 6-regular circulant graphs by four acyclic disconnected graphs.
Keywords
Orthogonal double covers of graphs, Labellings of graphs, Circulant graphs