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In the main this paper introduces the concept of chromatic harmonic polynomials denoted, H (G; x) and chromatic harmonic indices denoted, H (G) of a graph G. The new concept is then applied to  nd-ing explicit formula for the minimum (maximum) chromatic harmonic polynomials and the minimum (maximum) chromatic harmonic index of certain graphs. It is also applied to split graphs and certain Derivative split graphs.

The set of all non-increasing non-negative integer sequences p= (d1, d2,…, dn) is denoted by NSn. A sequence pÎNSn is said to be graphic if it is the degree sequence of a simple graph G on nvertices, and such a graph G is called a realization of p The set of all graphic sequences in NSn is denoted by GSn. The complete product split graph on L+M vertices is denoted by `SL, M=KL Ú`KM, where KL and KM are complete graphs respectively on L=Σp i=1 ri and M=Σp i=1 si vertices with ri andsi being integers. Another split graph is denoted by SL, M=`Sr 1, s 1 Ú`Sr2, s 2 Ú…Ú`Srp, sp= (Kr1ÚKs1) _ (Kr2 Ú Ks2) Ú…Ú (Krp Ú Ksp). A sequence p= (d 1, d 2,… , dn) is said to be po-tentially SL, M -graphic (respectively SL, M) -graphic if there is a realization G of p containing `SL, M (respectively `SL, M) as a subgraph. If p has a realization G containing `SL, M on those vertices having degrees d1, d2,… , dL+M, then p is potentially AL, M -graphic. A non-increasing sequence of non-negative integersp= (d1, d2,…, dn) is potentially AL, M -graphic if and only if it is potentially SL, M -graphic. In this paper, we obtain the sufficient condition for a graphic sequence to be potentially AL, M -graphic and this result is a generalization of that given by J. H. Yin on split graphs.

The aim of the present study was the histological evaluation of Enamel Matrix Derivative (EMD) effectiveness for regeneration of periodontal defects. EMD activates cementum synthesis, PDL and bone during the maturation stage of follicole. In this research, EMD was used in surgical defects of premolar teeth in four adult sheep. Muccoperiosteal flap was reflected in buccal site of teeth. The buccal bone plate was removed from mesial to distal in 4 mm depth. After eliminating the cementum by bur and its etching, EMD was applied on exposed dentine and flap was sutured. In opposite sites of those teeth (control sites) the same process was performed without etching. After 100 days, sheep were sacrificed and histological study through light microscopic was performed on black sections of operation sites. The results showed that in test sites, regeneration of cementum and bone was 62/5% and 42/5-50% respectively. But in control sites regeneration of cementum and bone was 37.5% and 32/5-42/5% respectively. Also the migration of junctional epithelium in control sites was 8-10% more than test sites. The important point is that in test sites, cementum was completely attached to undermining dentine. But, in control sites, the gap between cementum and dentine was visible. As a result, this study suggests that EMD promotes periodontal regeneration, and EMD application is a successful achievement in regenerative periodontal therapy.

We report a case of an 87-year-old man where coronary CT angiography incidentally demonstrated a “split” right coronary artery (RCA) featuring a “split” posterior descending artery. This case focusses on the morphological description of this variant as well as its differentiation from a “dual” or “duplicated” RCA.

The independence graph Ind(G) of a graph G is the graph with vertices as maximum independent sets of G and two vertices are adjacent, if and only if the corresponding maximum independent sets are disjoint. In this work, we find the independence graph of Cartesian product of d copies of complete graphs Kq, which is known as the Hamming graph H(d, q). Greenwell and Lovasz [7] found that the independence number of direct product of d copies of Kq as qd−1. We prove that the independence number of Hamming graph H(d, q), which is cartesian product of d copies of Kq, is also qd−1. As an application of our findings, we find answers for rook problem in higher dimensional square chess board.

Background and Aim: Postoperative swelling and edema can cause distress to the patient due to considerable pain and, delayed healing. The purpose of this study was to evaluate the effect of sub mucosal injection of Dexamethasone on postoperative edema after BSSRO.Materials and Methods: The study design was double blind clinical trial in which 19 patients requiring BSSRO were informed and randomly placed into two groups, 11 patients in the case group received 8mg Dexamethasone as a submucosal injection and 9 patients in the control group received 8mg of intravenous injections. Standardized surgical protocols were performed by the same surgeon. Maximum distances from the tragus to the corner of the mouth and from the tragus to the pogonion were measured at baseline and 48 hours post-surgery. Statistical analysis was done using Mann-U-Whitney Test.Results: The study was done on 19 patients in two groups that were matched based on age, sex, weight, period of surgery, type and level of malocclusion and socio-economical state. The average distance from the tragus to the corner of the mouth was 12.8±3 in control group and 14.6±14.9 in case group (p<0.8). The average distance from the tragus to the pogonion was 10.5±3.2 in control group and 14.2±4.3 in case group (p<0.2).Conclusion: Submucosal injection of Dexamethasone is as effective as intravenous injection in reduction of post-operative edema after BSSRO.

In this paper, we find the star chromatic number of central graph of complete bipartite graph and corona graph of complete graph with path and cycle.