The feedback vertex set (FVS) problem is to find the set of vertices of minimum cardinality whose removal renders the graph acyclic. The FVS problem has applications in several areas such as combinatorial circuit desi...The feedback vertex set (FVS) problem is to find the set of vertices of minimum cardinality whose removal renders the graph acyclic. The FVS problem has applications in several areas such as combinatorial circuit design, synchronous systems, computer systems, and very-large-scale integration (VLSI) circuits. The FVS problem is known to be NP-hard for simple graphs, but polynomi-al-time algorithms have been found for special classes of graphs. The intersection graph of a collection of arcs on a circle is called a circular-arc graph. A normal Helly circular-arc graph is a proper subclass of the set of circular-arc graphs. In this paper, we present an algorithm that takes time to solve the FVS problem in a normal Helly circular-arc graph with n vertices and m edges.展开更多
The vertex connectivity k(G) of a graph G is the minimum number of nodes whose deletion disconnects it. Graph connectivity is one of the most fundamental problems in graph theory. In this paper, we designed an O(n2) t...The vertex connectivity k(G) of a graph G is the minimum number of nodes whose deletion disconnects it. Graph connectivity is one of the most fundamental problems in graph theory. In this paper, we designed an O(n2) time algorithm to solve connectivity problem on circular trapezoid graphs.展开更多
Let G= (V, E) be a graph and A(G) is the collection of all minimal equitable dominating set of G. The middle equitable dominating graph of G is the graph denoted by Med(G) with vertex set the disjoint union of V∪A(G)...Let G= (V, E) be a graph and A(G) is the collection of all minimal equitable dominating set of G. The middle equitable dominating graph of G is the graph denoted by Med(G) with vertex set the disjoint union of V∪A(G) and (u, v) is an edge if and only if u ∩ v ≠ φ whenever u, v ∈ A(G) or u ∈ v whenever u ∈ v and v ∈ A(G) . In this paper, characterizations are given for graphs whose middle equitable dominating graph is connected and Kp∈Med(G) . Other properties of middle equitable dominating graphs are also obtained.展开更多
The intersection number, in (G), has been defined as the minimumcardinality of a set S which has n different subsets S_i such that each S_i can beassigned to the node v_i of G and nodes v_i, v_j are adjacent if and on...The intersection number, in (G), has been defined as the minimumcardinality of a set S which has n different subsets S_i such that each S_i can beassigned to the node v_i of G and nodes v_i, v_j are adjacent if and onlyif S_i∩S_j ≠0. We introduce the multiset intersection number min (G), defined similarly exceptthat multisets with elements in S may now be assigned to the nodes of G. Weprove that min (G) equals the smallest number ofcliques of G whose union is G.展开更多
文摘The feedback vertex set (FVS) problem is to find the set of vertices of minimum cardinality whose removal renders the graph acyclic. The FVS problem has applications in several areas such as combinatorial circuit design, synchronous systems, computer systems, and very-large-scale integration (VLSI) circuits. The FVS problem is known to be NP-hard for simple graphs, but polynomi-al-time algorithms have been found for special classes of graphs. The intersection graph of a collection of arcs on a circle is called a circular-arc graph. A normal Helly circular-arc graph is a proper subclass of the set of circular-arc graphs. In this paper, we present an algorithm that takes time to solve the FVS problem in a normal Helly circular-arc graph with n vertices and m edges.
文摘The vertex connectivity k(G) of a graph G is the minimum number of nodes whose deletion disconnects it. Graph connectivity is one of the most fundamental problems in graph theory. In this paper, we designed an O(n2) time algorithm to solve connectivity problem on circular trapezoid graphs.
文摘Let G= (V, E) be a graph and A(G) is the collection of all minimal equitable dominating set of G. The middle equitable dominating graph of G is the graph denoted by Med(G) with vertex set the disjoint union of V∪A(G) and (u, v) is an edge if and only if u ∩ v ≠ φ whenever u, v ∈ A(G) or u ∈ v whenever u ∈ v and v ∈ A(G) . In this paper, characterizations are given for graphs whose middle equitable dominating graph is connected and Kp∈Med(G) . Other properties of middle equitable dominating graphs are also obtained.
文摘The intersection number, in (G), has been defined as the minimumcardinality of a set S which has n different subsets S_i such that each S_i can beassigned to the node v_i of G and nodes v_i, v_j are adjacent if and onlyif S_i∩S_j ≠0. We introduce the multiset intersection number min (G), defined similarly exceptthat multisets with elements in S may now be assigned to the nodes of G. Weprove that min (G) equals the smallest number ofcliques of G whose union is G.
