Connected and two-connected graphs
Structure and enumeration of two-connected graphs with prescribed three-connected components
... we see the 3-components appearing: the 3-connected components A, B, and C, and the polygons P , T and U . The above dissection could also be performed for the separating pairs {a, e} or {c, e}, for example, but ...
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Correlation Clustering and Two-edge-connected Augmentation for Planar Graphs
... and two-edge-connected survivability [13] for the variant in which the solution is allowed to include multiple copies of edges of the input ...to two-edge-connected augmentation is that ...
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Enumerating all connected maximal common subgraphs in two graphs
... comparing two proteins without using any addi- tional information which is used for placing a seed before starting the comparison at the atomic description ...labelled graphs, where the vertices represent ...
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2 1-connected cubic graphs
... A well-known conjecture of Berge and Fulkerson [9] can be stated as follows: Conjecture 1 (Berge-Fulkerson). Let G be a 3-graph. There exist six perfect match- ings of G such that each edge of G belongs to exactly ...
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The edge domination number of connected graphs
... to graphs that are simple and ...every two distinct vertices of G are ...into two subsets U and W , called partite sets, such that every edge of G joins a vertex of U and a vertex of W ...
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The Largest Bond in 3-Connected Graphs
... Theorem 8. The circular ladder is dual Hamiltonian. Proof. Let G be a circular ladder graph with 2n vertices where n 3. G will have 3n edges. We can partition of the vertices of G into two sets, each of which ...
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Connected Edge Domination in Fuzzy Graphs
... the connected edge domination number of fuzzy graph using fuzzy edge cardinality and establish the relationship with other parameter which is also ...with two functions, σ : V → [0, 1] and µ : E → [0, 1] ...
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Triple Connected Domination In Directed Graphs
... be two distinct strong components of a quasi-transitive digraph D with atleast one arc from A to ...be two distinct strong components with an arc from A to ...
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On temporally connected graphs of small cost.
... the two incident edges of any w ∈ V , one g connecting it to a vertex in D 1 and one r connecting it to a vertex in D 2 , and still satisfy the property ...
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Quadrangularly connected claw-free graphs
... C − [x j , x i ] = (x j x j−1 . . . x i ). An edge e = uv is called a chord of C if e /∈ E(C) and u and v are on C. If a cycle C has no chords, then we say that C is chord-free. Obviously, 3-cycles are chord-free. The ...
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On connected k-domination numbers of graphs
... with two vertices being adjacent if and only if the corresponding street intersections are a block ...minimum connected k-dominating set in G may be used to consider the location of a minimum number of ...
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Testing the simultaneous embeddability of two graphs whose intersection is a biconnected or a connected graph
... Fig. 6. The gadget of a node of μ that is not an S-node, represented as a thick gray edge. The thin edges attaching to μ are the exclusive edges of μ . After the transformation they are attached to either μ or r μ . ...
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Strong weakly connected domination subdivisible graphs
... Theorem 4 A tree T is strong-γ w -1-subdivisible if and only if T belongs to the fam- ily T . Proof. Let T belong to the family T . Then T is obtained from a star K 1,s , s ≥ 2, using p times operation Y and, from ...
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The flip Markov chain for connected regular graphs
... • If a bridge change is required in H j then perform the bridge change. In that case, v j v j ′ is one of the edges forming the 2-edge-cut, so all other neighbours of v j must lie in B 1 . Therefore the new exit vertex v ...
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The complexity of optimal design of temporally connected graphs.
... of two vertices u, v ∈ V (G) is exactly m, then to reach v from u via a temporal path in the temporal graph on G, we need to move through vertices by consecutively swapping the bits in which u and v differ in the ...
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Connected End Equitable Domination In Fuzzy Graphs
... any connected fuzzy G is not isomorphic to . Proof Let be a connected fuzzy graph with order ...atleast two equitable adjacent vertices and have the strong edges then { } or { } is end equitable ...
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The Complexity of Optimal Design of Temporally Connected Graphs
... temporal graphs As mentioned earlier, if many edges have the same label, we can encounter trivial cases of minimal temporal ...temporal graphs, in which every edge only becomes available at one moment in ...
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Connected Total Global Domination in Fuzzy Graphs
... A dominating set is called anindependent dominating set if D is independent. An independent dominating set S of a fuzzy graph G is said to be amaximal independent dominating set if there is no independent dominating set ...
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The maximal total irregularity of some connected graphs
... unicyclic graphs and determined the graph with the maximal total irregularity among all unicyclic graphs on ...introduced two transformations to study the total irregularity of bicyclic graphs ...
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