✦ LIBER ✦

Three New Distance-regular Graphs

✍ Scribed by Leonard H. Soicher

Publisher: Elsevier Science
Year: 1993
Tongue: English
Weight: 160 KB
Volume: 14
Category: Article
ISSN: 0195-6698
DOI: 10.1006/eujc.1993.1052

No coin nor oath required. For personal study only.

📜 SIMILAR VOLUMES

Bipartite distance-regular graphs of val

Bipartite distance-regular graphs of valency three

✍ Tatsuro Ito 📂 Article 📅 1982 🏛 Elsevier Science 🌐 English ⚖ 788 KB

A new inequality for distance-regular gr

A new inequality for distance-regular graphs

✍ Paul Terwilliger 📂 Article 📅 1995 🏛 Elsevier Science 🌐 English ⚖ 521 KB

Given a nontrivial primitive idempotent E of a distance-regular graph/-with diameter d ~> 3, we obtain an inequality involving the intersection numbers of F for each integer i (3 ~< i ~< d). We show equality is attained for i = 3 if and only if equality is attained for all i (3 ~< i ~< d) if and onl

A new condition for distance-regular gra

A new condition for distance-regular graphs

✍ J.H. Koolen 📂 Article 📅 1992 🏛 Elsevier Science 🌐 English ⚖ 109 KB

From regular boundary graphs to antipoda

From regular boundary graphs to antipodal distance-regular graphs

✍ Fiol, M. A.; Garriga, E.; Yebra, J. L. A. 📂 Article 📅 1998 🏛 John Wiley and Sons 🌐 English ⚖ 383 KB 👁 2 views

Let Γ be a regular graph with n vertices, diameter D, and d + 1 In a previous paper, the authors showed that if P (λ) > n -1, then D ≤ d -1, where P is the polynomial of degree d-1 which takes alternating values ±1 at λ 1 , . . . , λ d . The graphs satisfying P (λ) = n -1, called boundary graphs, h

A new feasibility condition for distance

A new feasibility condition for distance-regular graphs

✍ Paul Terwilliger 📂 Article 📅 1986 🏛 Elsevier Science 🌐 English ⚖ 228 KB

Let F be a distance-regular graph with valency k (k >I 2) and diameter at least 2, and denote by ;t 1 and 2%~m the second largest and least eigenvalue of F, respectively. Assume the multiplicity m( )O of some eigenvalue ;~ ( )~ :/: k) of F satisfies m( Z ) < k. Then ;~ = Z 1 or )'rot. and either (i)

Resistance distance in regular graphs

✍ I. Lukovits; S. Nikolić; N. Trinajstić 📂 Article 📅 1999 🏛 John Wiley and Sons 🌐 English ⚖ 240 KB 👁 2 views

This report considers the resistance distance as a recently proposed new ## Ž . intrinsic metric on molecular graphs, and in particular, the sum R over resistance distances between all pairs of vertices is considered as a graph invariant. It has been vertices and K denotes a complete graph contai