On Strongly Regular Graphs with /m2 - m3/ ≤ 3

Lepović, Mirko
July 2010
Global Journal of Pure & Applied Mathematics;2010, Vol. 6 Issue 2, p125
Academic Journal
We say that a regular graph G of order n and degree r ≥ 1 (which is not the complete graph) is strongly regular if there exist non-negative integers τ and θ such that /Si ∩ Sj / = τ for any two adjacent vertices I and j , and /SI ∩ Sj/= θ for any two distinct non-adjacent vertices I and j , where Sk denotes the neighborhood of the vertex k. Let λ1 = r, λ2 and λ3 be the distinct eigenvalues of a connected strongly regular graph. Let m1 = 1, m2 and m3 denote the multiplicity of r, λ2 and λ3, respectively. We here describe the parameters n, r, τ and θ for strongly regular graphs with /m2 - m3/ ≤ 3.


Related Articles

  • On the Existence of Noncritical Vertices in Digraphs. Nenashev, G. // Journal of Mathematical Sciences;Feb2014, Vol. 196 Issue 6, p791 

    Let D be a strongly connected digraph on n ≥ 4 vertices. A vertex v of D is noncritical if the digraph D − v is strongly connected. It is proved that if the sum of degrees of any two adjacent vertices of D is at least n + 1, then there exists a noncritical vertex in D, and if the...

  • THE VERTEX DETOUR HULL NUMBER OF A GRAPH. Santhakumaran, A. P.; Chandran, S. V. Ullas // Discussiones Mathematicae: Graph Theory;2012, Vol. 32 Issue 3, p321 

    For vertices x and y in a connected graph G, the detour distance D (x, y) is the length of a longest x-y path in G. An x-y path of length D (x, y) is an x-y detour. The closed detour interval ID[x, y] consists of x, y, and all vertices lying on some x-y detour of G; while for S ⊆ V (G),...

  • The Existence of an Alternating Sign on a Spanning Tree of Graphs. KIM, DONGSEOK; KWON, YOUNG SOO; LEE, JAEUN // Kyungpook Mathematical Journal;Dec2012, Vol. 52 Issue 4, p513 

    For a spanning tree T of a connected graph .. and for a labelling Φ: E(T ) ! {+,-}, Φ is called an alternating sign on a spanning tree T of a graph ... if for any cotree edge e ∈ E(...)-E(T ), the unique path in T joining both end vertices of e has alternating signs. In the present...

  • Spanning $$k$$ -Forests with Large Components in $$K_{1,k+1}$$ -Free Graphs. Ozeki, Kenta; Sugiyama, Takeshi // Graphs & Combinatorics;Sep2015, Vol. 31 Issue 5, p1659 

    For an integer $$k$$ with $$k \ge 2$$ , a $$k$$ - tree (resp. a $$k$$ - forest) is a tree (resp. forest) with maximum degree at most $$k$$ . In this paper, we show that for any integer $$k$$ with $$k \ge 3$$ , any connected $$K_{1,k+1}$$ -free graph has a spanning $$k$$ -tree or a spanning $$k$$...

  • Trees preserving Wiener index in two classes of graphs. JIANG Zhen-ying; WANG Li-gong // Basic Sciences Journal of Textile Universities / Fangzhi Gaoxia;jun2013, Vol. 26 Issue 2, p176 

    The existence problem on trees preserving the Wiener index of two classes of graphs is studied in this paper. The Wiener index W(G) of a connected graph G is the sum of distances among all pairs of vertices in G. If there is a connected subtree T of a given connected graph G such that W(G)...

  • On conjectures and problems of Ruzsa concerning difference graphs of S-units. Ćustić, A.; Hajdu, L.; Kreso, D.; Tijdeman, R. // Acta Mathematica Hungarica;Aug2015, Vol. 146 Issue 2, p391 

    Given a finite nonempty set of primes S, we build a graph $${\mathcal{G}}$$ with vertex set $${\mathbb{Q}}$$ by connecting $${x, y \in \mathbb{Q}}$$ if the prime divisors of both the numerator and denominator of x − y are from S. In this paper we resolve two conjectures posed by Ruzsa...

  • 4-Cycle Systems of $$K_n - E(F^*)$$. Sehgal, Nidhi; Rodger, C. // Graphs & Combinatorics;Sep2015, Vol. 31 Issue 5, p1703 

    In this paper necessary and sufficient conditions are found for the existence of a $$4$$ -cycle system of a complete graph on $$n$$ vertices with leave a nearly $$2$$ -regular graph (that is, a not necessarily spanning graph in which all vertices have degree 2 except for one of degree greater...

  • Degree-Constrained Graph Orientation: Maximum Satisfaction and Minimum Violation. Asahiro, Yuichi; Jansson, Jesper; Miyano, Eiji; Ono, Hirotaka // Theory of Computing Systems;Jan2016, Vol. 58 Issue 1, p60 

    A degree-constrained graph orientation of an undirected graph G is an assignment of a direction to each edge in G such that the outdegree of every vertex in the resulting directed graph satisfies a specified lower and/or upper bound. Such graph orientations have been studied for a long time and...

  • Security of scale-free networks. Gała̧zka, M.; Szymański, J. // Journal of Mathematical Sciences;Apr2012, Vol. 182 Issue 2, p200 

    An important property of a scale-free network which allows one to communicate between its nodes is the connectivity. From the simulation results it is known that such networks are resistant to random damage. It is also known from experiments that usually disconnecting such a graph is obtained by...


Read the Article


Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics