Results 41 to 50 of about 3,086,920 (343)
Al-Rafidain Journal of Computer Sciences and Mathematics, 2023 The new distance defined on a connected graph G contains of three terms: The ordinary distance between any two vertices in G, both the sum and the product of the two vertices' degrees, as this distance is more useful than the ordinary distance ...
Asmaa Aziz
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Electronic Journal of Graph Theory and Applications, 2015 The reciprocal complementary distance (RCD) matrix of a graph $G$ is defined as $RCD(G) = [rc_{ij}]$ where $rc_{ij} = \frac{1}{1+D-d_{ij}}$ if $i \neq j$ and $rc_{ij} = 0$, otherwise, where $D$ is the diameter of $G$ and $d_{ij}$ is the distance between ...
Harishchandra S. Ramane +1 more
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AUTOMORPHISMS OF DISTANCE-REGULAR GRAPH WITH INTERSECTION ARRAY {25; 16; 1; 1; 8; 25}
Ural Mathematical Journal, 2017 Makhnev and Samoilenko have found parameters of strongly regular graphs with no more than 1000 vertices, which may be neighborhoods of vertices in antipodal distance-regular graph of diameter 3 and with \(\lambda=\mu\).
Konstantin S. Efimov +1 more
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Automorphism groups of the constituent graphs of integral distance graphs
AKCE International Journal of Graphs and Combinatorics, 2023 In this paper, we consider the automorphism groups of Cayley graphs which are a basis of a complete Boolean algebra of strongly regular graphs, one of such graph is the integral distance graph [Formula: see text] The automorphism groups of the integral ...
O. Habineza, E. Mwambene
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On the Cheeger constant for distance-regular graphs [PDF]
Journal of Combinatorial Theory, 2018 The Cheeger constant of a graph is the smallest possible ratio between the size of a subgraph and the size of its boundary. It is well known that this constant must be at least $\frac{\lambda_1}{2}$, where $\lambda_1$ is the smallest positive eigenvalue ...
Zhi Qiao, J. Koolen, Greg Markowsky
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On Automorphisms of a Distance-Regular Graph with Intersection Array {125,96,1;1,48,125} [PDF]
Учёные записки Казанского университета: Серия Физико-математические науки, 2017 J. Koolen posed the problem of studying distance-regular graphs in which neighborhoods of vertices are strongly regular graphs with the second eigenvalue ≤ t for the given positive integer t.
V.V. Bitkina, A.A. Makhnev
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Distance-regular graphs without 4-claws [PDF]
European journal of combinatorics (Print), 2017 We determine the distance-regular graphs with diameter at least $3$ and $c_2\geq 2$ but without induced $K_{1,4}$-subgraphs.
S. Bang +2 more
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On Subgraphs in Distance-Regular Graphs [PDF]
Journal of Algebraic Combinatorics, 1992 A graph is distance-regular when it is simple and for any two vertices at distance \(j\), the numbers of vertices adjacent to one and at distance \(j- 1\) (resp. \(j\) and \(j+1)\) of the other are constant (depending on \(j\) only). First some necessary conditions are derived for distance- regularity of the subgraph of the geodesics joining two ...
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On one infinite series of admissible intersection arrays of distance-regular graphs of diameter 5
Известия высших учебных заведений. Поволжский регион: Физико-математические науки, 2022 Background. One generalization of one known infinite series of admissible intersection arrays of a bipartite antipodal distance-regular graph is proposed for consideration.
I.T. Mukhamet'yanov
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A Characterization of Q-Polynomial Distance-Regular Graphs Using the Intersection Numbers [PDF]
Graphs Comb., 2017 We consider a primitive distance-regular graph $$\varGamma $$Γ with diameter at least 3. We use the intersection numbers of $$\varGamma $$Γ to find a positive semidefinite matrix G with integer entries. We show that G has determinant zero if and only if $
Supalak Sumalroj
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