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113.548  Articles
1 of 11.356 pages  |  10  records  |  more records»
For any two vertices u and v in a connected graph G = (V, E), a u - v path P is called a u - v triangle free path if no three vertices of P induce a triangle. The triangle fre... see more

For a connected graph G = (V, E) of order at least three, the monophonic distance dm(u, v) is the length of a longest u - v monophonic path in G. A u - v path of length dm(u, v) is called a u - v detour monophonic. For subsets A and B of V, the m-monophon... see more

Let ?(G) denote the number of components of a graph G. A connected graph G is said to be 1-tough if ?(G - X)=|X| for all X ? V(G) with ?(G - X)>1. It is well-known that every hamiltonian graph is 1-tough, but that the... see more

We compute the Betti numbers for all the powers of initial and final lexsegment edge ideals. For the powers of the edge ideal of an anti–d-path, we prove that they have linear quotients and we characterize the normally torsion–free ideals. We determine a ... see more

For a connected graph G = (V, E) of order at least two, a chord of a path P is an edge joining two non-adjacent vertices of P. A path P is called a monophonic path if it is a chordless path. A longest x – y monophonic path is called an x – y detour monoph... see more

A hole in a graph GG is an induced cycle of length at least four, and an even hole is a hole of even length. The diamond is the graph obtained from the complete graph K4K_4 by removing an edge. A pyramid is a graph consisting of a vertex aa called the&nbs... see more

For a connected graph G of order at least two, a path P is called a monophonic path if it is a chordless path. A longest x — y monophonic path is called an x — y detour monophonic path. A set S of vertices of G is an edge detour monophonic set of G if eve... see more

For a connected graph G of order at least two, an edge detour monophonic set of G is a set S of vertices such that every edge of G lies on a detour monophonic path joining some pair of vertices in S. The edge detour monophonic number of G is the minimum c... see more

Seven spot ladybird beetle, (Coccinella septempunctata) is a widely distributed natural enemy of soft-bodied insect pests especially aphids worldwide. Both the adult and larvae of this coccinellid beetle are voracious feeders and serve as a commercially a... see more

1 of 11.356 pages  |  10  records  |  more records»