ar X iv : 0 90 1 . 13 57 v 2 [ m at h . C O ] 1 0 Ju l 2 00 9 A Characterization On Potentially K 2 , 5 - graphic Sequences ∗

ar X iv : 0 81 2 . 48 61 v 2 [ m at h . C O ] 8 J ul 2 00 9 On Potentially K 6 − C 5 graphic Sequences ∗

For given a graph H , a graphic sequence π = (d1, d2, · · · , dn) is said to be potentially H-graphic if there exists a realization of π containing H as a subgraph. In this paper, we characterize the potentially K6 − C5 -graphic sequences .

ar X iv : m at h / 07 02 24 5 v 1 [ m at h . C O ] 9 F eb 2 00 7 On Potentially K 5 − E 3 - graphic Sequences ∗

Let Km −H be the graph obtained from Km by removing the edges set E(H) of H where H is a subgraph of Km. We use the symbol A3 to denote P2 ∪K2. In this paper, we characterize the potentially K5 − P3, K5 −A3, K5 −K3 and K5 −K1,3-graphic sequences. Two characterizations of these imply two theorems due to Lai [11-12].

ar X iv : 0 90 5 . 27 40 v 1 [ m at h . C O ] 1 7 M ay 2 00 9 Graphs with many ± 1 or ± √ 2 eigenvalues

A pseudo (v, k, λ)-design is a pair (X,B) where X is a v-set and B = {B1, . . . , Bv−1} is a collection of k-subsets (blocks) of X such that each two distinct Bi, Bj intersect in λ elements; and 0 < λ < k < v − 1. We use the notion of pseudo designs to characterize graphs of order n whose spectrum contains either ±1 or ± √ 2 with multiplicity (n − 2)/2 or (n− 3)/2. It turns out that the subdivi...

ar X iv : 0 80 1 . 06 58 v 1 [ m at h . C O ] 4 J an 2 00 8 On Potentially 3 - regular graph graphic Sequences ∗

For given a graphH , a graphic sequence π = (d1, d2, · · · , dn) is said to be potentially H-graphic if there exists a realization of π containing H as a subgraph. In this paper, we characterize the potentially Hgraphic sequences where H denotes 3-regular graph with 6 vertices. In other words, we characterize the potentially K3,3 and K6 − C6graphic sequences where Kr,r is an r × r complete bipa...

ar X iv : m at h - ph / 0 60 70 40 v 1 2 0 Ju l 2 00 6 Invariant Form of BK - factorization and its Applications