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On the Weak Reconstruction of Strong Product Graphs
Electronic Notes in Discrete Mathematics, 2003 We prove that any nontrivial connected strong product graph can be uniquely reconstructed from each of its one vertex deleted subgraphs.
Blaz Zmazek, Janez Zerovnik
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NZ‐flows in strong products of graphs
Journal of Graph Theory, 2010 AbstractWe prove that the strong product G1⊠ G2 of G1 and G2 is ℤ3‐flow contractible if and only if G1⊠ G2 is not T⊠ K2, where T is a tree (we call T⊠ K2 a K4‐tree). It follows that G1⊠ G2 admits an NZ 3 ‐flow unless G1⊠ G2 is a K4 ‐tree. We also give a constructive proof that yields a polynomial algorithm whose output is an NZ 3‐flow if G1⊠ G2 is not ...
Wilfried Imrich +3 more
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Some Applications of Strong Product [PDF]
Mathematics Interdisciplinary Research, 2018 Let G and H be graphs. The strong product GH of graphs G and H is the graph with vertex set V(G)V(H) and u=(u1, v1) is adjacent with v= (u2, v2) whenever (v1 = v2 and u1 is adjacent with u2) or (u1 = u2 and v1 is adjacent with v2) or (u1 is adjacent ...
Mostafa Tavakoli +2 more
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Theory and Applications of Fermatean Neutrosophic Graphs [PDF]
Neutrosophic Sets and Systems, 2022 Yager et. al. defined a q-rung orthopair fuzzy sets as a new general class of Pythagorean fuzzy set in which the sum of the qth power of the support for and support against is bonded by one. Tapan et. al. extended the concept of intuitionistic fuzzy sets
Said Broumi +4 more
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Investigations in the semi-strong product of graphs and bootstrap percolation [PDF]
, 2023 The semi-strong product of graphs G and H is a way of forming a new graph from the graphs G and H. The vertex set of the semi-strong product is the Cartesian product of the vertex sets of G and H, V(G) x V(H).
McCall, Kevin J
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Numerical invariants and the strong product of graphs [PDF]
, 1973 Three numerical invariants of graphs—the independence number, the cliquecovering number, and the Rosenfeld number—are studied in relation to themselves and to the strong product of two graphs.
Hales, R.S
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A Novel Study of Graphs Based on m-Polar Cubic Structures
Journal of Function Spaces, 2022 By combining the notions of interval-valued m-polar fuzzy graphs and m-polar fuzzy graphs, the notion of m-polar cubic graphs is first introduced. Then, the degree of a vertex in m-polar cubic graphs and complete m-polar cubic graphs is defined.
G. Muhiuddin +4 more
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Bounds for the pebbling number of product graphs [PDF]
Transactions on Combinatorics, 2022 Let $G$ be a connected graph. Given a configuration of a fixed number of pebbles on the vertex set of $G$, a pebbling move on $G$ is the process of removing two pebbles from a vertex and adding one pebble on an adjacent vertex. The pebbling number of $G$,
Nopparat Pleanmani +2 more
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Strong Total Monophonic Problems in Product Graphs, Networks, and Its Computational Complexity
Journal of Mathematics, 2022 Let G be a graph with vertex set as VG and edge set as EG which is simple as well as connected. The problem of strong total monophonic set is to find the set of vertices T⊆VG, which contains no isolated vertices, and all the vertices in VG\T lie on a ...
Eddith Sarah Varghese +5 more
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The optimal strong radius and optimal strong diameter of the Cartesian product graphs [PDF]
, 2011 NSFC [10831001]; Fujian Provincial Department of Education [JA10244]Let D be a strong digraph. The strong distance between two vertices u and v in D. denoted by sd(D)(u.
郭晓峰 +3 more
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