Results 251 to 260 of about 473,067 (264)

On the Edge Connectivity of Semi-strong Product Graphs

Applied and Computational Mathematics
The concept of edge connectivity was first proposed by K. Menger, and in communication networks and logical networks, edge connectivity can be used to measure network reliability and fault tolerance.
Qiaoling Wang, Haizhen Ren
semanticscholar   +1 more source

Ricci Curvature of Strong Product Graphs

Taiwanese journal of mathematics
We establish for the first time the explicit curvature formulas for the horizontal and vertical edges of the strong product of two regular graphs. We complement this result with showing that there does not exist an analogous formula for the curvatures of
Gu-Fang Mou
semanticscholar   +1 more source

On the Genus of Strong Tensor Products of Graphs

Canadian Journal of Mathematics, 1976
The genus parameter for graphs has been studied extensively in recent years, with impetus given primarily by the Ringel-Youngs solution to the Heawood Map-coloring Problem [15]. This solution involved the determination of 𝛄(Kn), the genus of the complete graph Kn.
Garman, B. L., Ringeisen, R. D., White, A. T.   +2 more
openaire   +3 more sources

Hamiltonian threshold for strong products of graphs

Journal of Graph Theory, 2008
AbstractWe prove that the strong product of any at least ${({\rm ln}}\, {2})\Delta+{O}(\sqrt{\Delta})$ non‐trivial connected graphs of maximum degree at most Δ is pancyclic. The obtained result is asymptotically best possible since the strong product of ⌊(ln 2)D⌋ stars K1,D is not even hamiltonian. © 2008 Wiley Periodicals, Inc.
Daniel Král, Ladislav Stacho
openaire   +2 more sources

Strong product of factor-critical graphs

International Journal of Computer Mathematics, 2011
Strong product G1⊠ G2 of two graphs G1 and G2 has a vertex set V(G1)×V(G2) and two vertices (u1, v1) and (u2, v2) are adjacent whenever u1=u2 and v1 is adjacent to v2 or u1 is adjacent to u2 and v1=v2, or u1 is adjacent to u2 and v1 is adjacent to v2. We investigate the factor-criticality of G1⊠ G2 and obtain the following. Let G1 and G2 be connected m-
Zefang Wu, Xu Yang, Qinglin Yu
openaire   +1 more source

Weighted PI index of tensor product and strong product of graphs

Discret. Math. Algorithms Appl., 2020
The Weighted Padmakar–Ivan (PI) index of a connected, simple graph [Formula: see text] is given by [Formula: see text], where [Formula: see text] denotes the number of equidistant vertices of the edge [Formula: see text]. In this paper, weighted PI index
C. Gopika, J. Geetha, K. Somasundaram
semanticscholar   +1 more source

Hamilton cycles in strong products of graphs

Journal of Graph Theory, 2005
AbstractWe prove that the strong product of any n connected graphs of maximum degree at most n contains a Hamilton cycle. In particular, GΔ(G) is hamiltonian for each connected graph G, which answers in affirmative a conjecture of Bermond, Germa, and Heydemann. © 2005 Wiley Periodicals, Inc.
Daniel Král, Jana Maxová, Robert Sámal, Pavel Podbrdský   +3 more
openaire   +2 more sources

Signed b-matchings and b-edge covers of strong product graphs

Contributions Discret. Math., 2010
In this paper, we study the signed b-edge cover number and the signed b-matching number of a graph. Sharp bounds on these parameters of the strong product graphs are presented.
Changping Wang
semanticscholar   +1 more source

The Development of New Operations for Tensor Products of Product Fuzzy Graphs, Strong Product Fuzzy Graphs, and Complete Product Fuzzy Graphs

Sainmatika Jurnal Ilmiah Matematika dan Ilmu Pengetahuan Alam
The purpose of this study is to develop new properties of product fuzzy graphs in the form of tensor product operations. The research method used consists of a preliminary stage, a stage of defining and theorems, a stage of proving theorems and verifying
Fery Firmansah
semanticscholar   +1 more source

Omega Indices of Strong and Lexicographic Products of Graphs

Current Organic Synthesis
Background: The degree sequence of a graph is the list of its vertex degrees arranged in usually increasing order. Many properties of the graphs realized from a degree sequence can be deduced by means of a recently introduced graph invariant called omega invariant.
Medha Itagi Huilgol, Grace Divya D'Souza, Ismail Naci Cangul   +2 more
openaire   +3 more sources