No you are not eligible to get admission in Ph.D Computer Science course just after passing BSC computer science course .
For admission you PHD course you have to passed master level degree course in computer science stream.

is a Doctorate Computer Engineering course. The duration of the course is three years and it may extend to five years.

Eligibility
For admission in the PHD computer science course you have to passed M.Tech/M.Phil degree in Computer Science/Information Technology and you have to obtained minimum 55% for general category and 50% for SC/ST/PH candidates in master degree ..

For admission you have to qualify the entrance test conducted by college administration.

Colleges list for phd computer science :
Allahabad UniversitySenate Hall
Allahabad, Uttar Pradesh
Phone : (0532) 2462241, 2462242, 2462243, 2462244
Fax : (0532) 2462241

Amrita Vishwa Vidyapeetham - Coimbatore CampusEttimadai Post
Coimbatore, Tamil Nadu
Phone : (0422) 2685000
Fax : (0422) 2656274

Assam UniversitySilchar, Assam
Phone : (03842) 270806
Fax : (03842) 270826

Avinashilingam University for WomenMettupalatam Road
Coimbatore, Tamil Nadu
Phone : (0422) 2440241, 2435550, 2658145, 2658716
Fax : (0422) 2438786, 2441252

Babasaheb Bhimrao Ambedkar University (BBAU)Vidya Vihar, Rai Bareilly Road
Lucknow, Uttar Pradesh
Phone : (0522) 2440822
Mobile : 9415951864
Fax : (0522) 2440821, 2441888

Babu Banarasi Das University (BBDU)B.B.D. City, Faizabad Road
Lucknow, Uttar Pradesh
Phone : (0522) 3911000, 2815183, 28151186
Fax : (0522) 2815294, 3911111

Banasthali UniversityP.O.Banasthali Vidyapith
Tonk, Rajasthan
Phone : (01438) 228456, 228975, 228990
Fax : (01438) 228365

Bharati Vidyapeeth UniversityLal Bahadur Shastri Marg
Pune, Maharashtra
Phone : (020) 24407106, 24407114
Fax : (020) 24339121, 24321910

Bhavnagar UniversityGaurishanker Lake Road,
Bhavnagar, Gujarat
Phone : (0278) 2430002, 2430006, 2430007, 2511565, 2511566
Mobile : 9426906333
Fax : (0278) 2426706, 2430002

Biju Patnaik University of Technology (BPUT)Rourkela
Rourkela, Orissa
Phone : (0661) 2402560, Camp Off. Bhubaneswar: (0674) 2352223
Fax : (0661) 2402556, Fax: (0674) 2352329

Gauhati UniversityGopinath Bordoloi Nagar
Guwahati, Assam
Phone : (0361) 2700311, 2570262, 2570412, 2570408
Mobile : 9435107019, 9859208171
Fax : (0361) 2700311, 2675515

Goa UniversityTaleigao Plateau, Taleigao
North Goa, Goa
Phone : (0832) 6519001, 6519002, 6519003, 6519005, 6519006, 6519007
Mobile : 9422442577, 9422438813
Fax : (0832) 2451184, 2452889

Gulbarga UniversityJnana Ganga
Gulbarga, Karnataka
Phone : (08472) 263201, 263200, 263202
Mobile : 9448213398, 9986748423, 9844231934
Fax : (08472) 263205

Guru Ghasidas VishwavidyalayaMain Campus, Koni
Bilaspur, Chhattisgarh
Phone : (07752) 260283, 260353, 260209, 260204, 260356
Fax : (07752) 260148

Himachal Pradesh UniversityBoileauganj to Summer Hill,
Shimla, Himachal Pradesh
Phone : (0177) 2830273, 2830434, 2830445, 2830614, 2830635, 2831809, 283187
Fax : (0177) 2830775

Indian School of Mines UniversityDhanbad, Jharkhand
Phone : (0326) 2296559, 2296560, 2296561, 2296562
Mobile : 9430352782
Fax : (0326) 2296563

Sir Padampat Singhania UniversityBhatewar Tehsil- Vallabhnagar. City Office- C/O J.K. Cement Ltd. Hill Villa Annexe Opp. Hilltop Palace Hotel Ambavgarh
Udaipur, Rajasthan
Phone : (02957) 226095
Mobile : 992883818
Fax : (02957) 226094

Solapur UniversitySolapur-Pune National Highway, Kegaon
Solapur, Maharashtra
Phone : (0217) 2351300, 2744776, 2744777
Fax : (0217) 2351300, 2744770

South Asian University (SAU)Akbar Bhawan Chanakyapuri
New Delhi, Delhi
Phone : (011) 24122512, 24122513, 24122514
Fax : (011) 24122511

University of Delhi (DU)Delhi, Delhi
Phone : (011) 27667011, 27667190
Fax : (011) 27667049

University of HyderabadGachibowli
Hyderabad, Andhra Pradesh
Phone : (040) 23130000, 23132101, 23132102, 23132103
Fax : (040) 23010292, 23130000

University of PuneGaneshkhind
Pune, Maharashtra
Phone : (020) 25601099, 25696061, 25690062, 25696064, 25696065
Fax : (020) 25690794

Utkal UniversityVanivihar
Bhubaneswar, Orissa
Phone : (0674) 252520

Vidyasagar UniversityPaschim Medinipur
Midnapore, West Bengal
Phone : (03222) 275297, 275441
Fax : (03222) 275297

Virudhunagar Hindu Nadar's Senthikumara Nadar CollegeVirudhunagr, Tamil Nadu
Phone : (04562) 280154
Fax : (04562) 281338

Visvesaraya National Institute of Technology - VNIT NagpurSouth Ambazari Road
Nagpur, Maharashtra
Phone : (0712) 2222828, 2224123, 2231636, 2226750, 2223710, 2236330
Mobile : 9422802995
Fax : (0712) 2223230, 2223969

Vivekanandha College of Engineering for WomenVivekanandha Educational Institutions, Elayampalayam, Tiruchengode
Namakkal, Tamil Nadu
Phone : (04288) 234060, 234670
Mobile : 9443734670, 9965534670
Fax : (04288) 234894, 234891